Design

Ecosystem size is a key factor driving biodiversity and ecosystem function. Larger ecosystems contain more species and can be hubs of dispersal and resource flows in networks of multiple ecosystems. However, whether and how ecosystem size and resource flows interact to affect biodiversity and ecosystem function has been largely overlooked. Here, we investigated how ecosystem size asymmetry affects biodiversity and function of two-ecosystem meta-ecosystems connected through flows of non-living resources. We conducted microcosm experiments, mimicking resource flows between ecosystems of different sizes, yet otherwise being identical. We found that meta-ecosystems with asymmetric ecosystem sizes had higher β-diversity but lower α-diversity and ecosystem function (total biomass) than their unconnected counterparts, while such an effect was not found for meta-ecosystems of identical ecosystem sizes. Our work demonstrates of how cross-ecosystem dynamics modulated by differences in ecosystem sizes affect biodiversity and function, with a direct implication for conservation and management of connected ecosystems.

Parameters

# --- SET UP R MARKDOWN AND GENERAL CODING RUNNING PARAMETERS --- #

set.seed(420)
start_time = Sys.time()
knitr::opts_chunk$set(message = FALSE,
                      cache = FALSE,
                      autodep = FALSE)
recompute_lengthy_analyses = FALSE
plot_model_residuals_metaecos = FALSE
# --- SET UP PARAMETERS RELATED TO RESOURCE FLOWS --- #

disturbance_levels = c("low", "high")
n_disturbance_levels = length(disturbance_levels)

resource_flow_days = c(5, 9, 13, 17, 21, 25)
first_resource_flow = resource_flow_days[1]
# --- SET UP SAMPLING PARAMETERS --- #

total_frames = 125
volume_recorded_μl = 34.4
time_points = 0:7
time_points_without_t0 = 1:7
time_point_names = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")
sampling_days = c(0, 4, 8, 12, 16, 20, 24, 28)
first_time_point = 0
last_time_point = length(sampling_days) - 1
n_time_points = last_time_point + 1
nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2) #Videos taken for each time point for each culture. At t0 we took 12 videos of the large bottle from which we started the  cultures. Write why 2 at the end. 

videos_taken = data.frame(time_point = 0 : 7,
                          nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2))

n_videos_taken_t0 = nr_videos[1]

time_point_day = data.frame(time_point = first_time_point:last_time_point,
                            day = sampling_days,
                            video_replicates = nr_videos)

videos_to_take_off = data.frame(culture_ID = NA,
                                time_point = NA,
                                file = NA) %>%
                     add_row(culture_ID = 137-110, 
                             time_point = 7, 
                             file = 137) %>%
                     slice(-1)

n_cultures = 110
total_number_of_video_rows = sum(nr_videos * n_cultures)
# --- SET UP PROTIST PARAMETERS --- #

protist_species = c("Ble", "Cep", "Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi", "Spi_te", "Tet")
protist_species_indiv_per_volume = paste0(protist_species, "_indiv_per_volume")
protist_species_indiv_per_ml = paste0(protist_species, "_indiv_per_ml")
protist_species_dominance = paste0(protist_species_indiv_per_ml, "_dominance")
protist_species_total = paste0(protist_species, "_tot_indiv")
n_protist_species = length(protist_species)
first_protist = protist_species[1]
last_protist = protist_species[n_protist_species]
species_IDD_with_13_threshold = c("Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi_te", "Tet")
species_IDD_with_13_threshold_indiv_per_volume = paste0(species_IDD_with_13_threshold, "_indiv_per_volume")
species_IDD_with_40_threshold = c("Ble", "Cep", "Spi")
species_IDD_with_40_threshold_indiv_per_volume = paste0(species_IDD_with_40_threshold, "_indiv_per_volume")
# --- SET UP ECOSYSTEM PARAMETERS --- #

ecosystems_to_take_off = 60 #Culture ID = 60 as it was spilled (small unconnected, high disturbance, system nr = 40)
ecosystems_info = read.csv(here("1_data", "ecosystems_info.csv"), header = TRUE)

columns_ecosystems = c("time_point",
                       "day",
                       "culture_ID",
                       "system_nr",
                       "disturbance",
                       "ecosystem_type",
                       "connection",
                       "ecosystem_size",
                       "ecosystem_size_ml",
                       "metaecosystem",
                       "metaecosystem_type")
columns_treatments = columns_ecosystems[!columns_ecosystems %in% c("system_nr", "culture_ID")]

variables_ecosystems = c("bioarea_mm2_per_ml",
                         "bioarea_tot_mm2",
                         "indiv_per_ml",
                         "indiv_tot",
                         "species_richness",
                         "shannon",
                         "simpson",
                         "inv_simpson",
                         "evenness_pielou",
                         "median_body_area_µm2",
                         paste0(protist_species, "_indiv_per_ml"),
                         paste0(protist_species, "_tot_indiv"),
                         paste0(protist_species_indiv_per_ml, "_dominance"))
baseline_columns = paste0("baseline_", variables_ecosystems)

ecosystem_types_ordered = c("Small connected to large",
                        "Small connected to small",
                        "Small unconnected",
                        "Medium connected to medium",
                        "Medium unconnected",
                        "Large connected to small",
                        "Large connected to large",
                        "Large unconnected")

treatments_and_controls = data.frame(treatment = c("Small connected to small",
                                                   "Small connected to large",
                                                   "Medium connected to medium",
                                                   "Large connected to large",
                                                   "Large connected to small"),
                                     control = c("Small unconnected",
                                                 "Small unconnected",
                                                 "Medium unconnected",
                                                 "Large unconnected",
                                                 "Large unconnected"))

n_treatments = length(unique(treatments_and_controls$treatment))
n_controls = length(unique(treatments_and_controls$control))
n_replicates = 5
n_ecosystem_types = 8
# --- SET UP SIZE CLASSES PARAMETERS --- #

n_size_classes = 12
columns_classes = c(columns_ecosystems,
                    "size_class_n",
                    "mean_class_area_µm2")
# --- SET UP META-ECOSYSTEM PARAMETERS --- #

metaecosystems_to_take_off = ecosystems_info %>%
  filter(culture_ID %in% ecosystems_to_take_off) %>%
  pull(system_nr) %>%
  unique

system_nr_metaecosystems = ecosystems_info %>%
  filter(metaecosystem == "yes") %>%
  pull(system_nr) %>%
  unique

n_metaecosystems = length(system_nr_metaecosystems)

variables_metaecos = c("total_metaecosystem_bioarea_mm2",
                       "jaccard_index",
                       "bray_curtis",
                       "beta_spatial_turnover",
                       "beta_nestedness",
                       "beta_total",
                       "metaecosystem_richness")

metaecosystem_types_ordered = c("Small-Small meta-ecosystem",
                                "Medium-Medium meta-ecosystem",
                                "Medium-Medium unconnected",
                                "Large-Large meta-ecosystem",
                                "Small-Large meta-ecosystem",
                                "Small-Large unconnected")

metaecosystem_type_selected = c("Medium-Medium",
                                "Small-Large")

Name of the axes per response variable.

# --- SET UP AXES LABELS PARAMETERS --- #

axis_names = data.frame(variable = NA,
                        axis_name= NA) %>%
  add_row(variable = "day", axis_name = "Time (day)") %>%
  add_row(variable = "ecosystem_size_ml", axis_name = "Patch size (ml)") %>%
  add_row(variable = "log_size_class", axis_name = "Log size (μm2)") %>%
  add_row(variable = "class_indiv_per_µl", axis_name = "Density (ind/ml)") %>%
  add_row(variable = "bioarea_mm2_per_ml", axis_name = "Biomass (mm2/ml)") %>%
  add_row(variable = "sqrt_bioarea_mm2_per_ml", axis_name = "Sqrt Biomass (mm2/ml)") %>%
  add_row(variable = "bioarea_mm2_per_ml_d", axis_name = "Bioamass ES") %>%
  add_row(variable = "bioarea_tot", axis_name = "Total Biomass (mm2)") %>%
  add_row(variable = "total_metaecosystem_bioarea_mm2", axis_name = "Total Biomass (mm2)") %>%
  add_row(variable = "species_richness", axis_name = "Species Richness") %>%
  add_row(variable = "species_richness_d", axis_name = "Species Richness ES") %>%
  add_row(variable = "mean_richness", axis_name = "Mean α-Diversity (Shannon)") %>%
  add_row(variable = "mean_shannon", axis_name = "Mean α-Diversity (Shannon)") %>%
  add_row(variable = "shannon", axis_name = "Biodiversity (Shannon)") %>%
  add_row(variable = "sqrt_shannon", axis_name = "Sqrt Biodiversity (Shannon)") %>%
  add_row(variable = "shannon_d", axis_name = "Biodiversity ES (Shannon ES)") %>%
  add_row(variable = "bray_curtis", axis_name = "β-Diversity (Bray-Curtis)") %>%
  add_row(variable = "beta_spatial_turnover", axis_name = "Turn over (Simpson pair-wise dissimilarity)") %>%
  add_row(variable = "beta_nestedness", axis_name = "Nestedness (nestedness-fraction of Sorensen)") %>%
  add_row(variable = "beta_total", axis_name = "Tot β-Diversity (Sorensen)") %>%
  add_row(variable = "metaecosystem_richness", axis_name = "γ-Diversity (Species Richness)") %>%
  add_row(variable = "indiv_per_ml", axis_name = "Abundance (ind/ml)") %>%
  add_row(variable = "indiv_per_ml_d", axis_name = "Abundance ES") %>%
  add_row(variable = "median_body_area_µm2", axis_name = "Median Body Size (µm²)") %>%
  add_row(variable = "median_body_area_µm2_d", axis_name = "Median Body Size ES") %>%
  add_row(variable = "Ble_indiv_per_ml", axis_name = "Ble Density (ind/ml)") %>% 
  add_row(variable = "Cep_indiv_per_ml", axis_name = "Cep Density (ind/ml)") %>%
  add_row(variable = "Col_indiv_per_ml", axis_name = "Col Density (ind/ml)") %>%
  add_row(variable = "Eug_indiv_per_ml", axis_name = "Eug Density (ind/ml)") %>%
  add_row(variable = "Eup_indiv_per_ml", axis_name = "Eup Density (ind/ml)") %>%
  add_row(variable = "Lox_indiv_per_ml", axis_name = "Lox Density (ind/ml)") %>%
  add_row(variable = "Pau_indiv_per_ml", axis_name = "Pau Density (ind/ml)") %>%
  add_row(variable = "Pca_indiv_per_ml", axis_name = "Pca Density (ind/ml)") %>%
  add_row(variable = "Spi_indiv_per_ml", axis_name = "Spi Density (ind/ml)") %>%
  add_row(variable = "Spi_te_indiv_per_ml", axis_name = "Spi te Density (ind/ml)") %>%
  add_row(variable = "Tet_indiv_per_ml", axis_name = "Tet Density (ind/ml)") %>%
  add_row(variable = "auto_hetero_ratio", axis_name = "Photosynthetisers-Heterotrops Ratio") %>%
  add_row(variable = "sqrt_auto_hetero_ratio", axis_name = "Sqrt Photosynthetisers-Heterotrops Ratio") %>%
  add_row(variable = "Ble_indiv_per_ml_d", axis_name = "Ble Density ES") %>%
  add_row(variable = "Cep_indiv_per_ml_d", axis_name = "Cep Density ES") %>%
  add_row(variable = "Col_indiv_per_ml_d", axis_name = "Col Density ES") %>%
  add_row(variable = "Eug_indiv_per_ml_d", axis_name = "Eug Density ES") %>%
  add_row(variable = "Eup_indiv_per_ml_d", axis_name = "Eup Density ES") %>%
  add_row(variable = "Lox_indiv_per_ml_d", axis_name = "Lox Density ES") %>%
  add_row(variable = "Pau_indiv_per_ml_d", axis_name = "Pau Density ES") %>%
  add_row(variable = "Pca_indiv_per_ml_d", axis_name = "Pca Density ES") %>%
  add_row(variable = "Spi_indiv_per_ml_d", axis_name = "Spi Density ES") %>%
  add_row(variable = "Spi_te_indiv_per_ml_d", axis_name = "Spi te Density ES") %>%
  add_row(variable = "Tet_indiv_per_ml_d", axis_name = "Tet Density ES") %>%
  add_row(variable = "Ble_indiv_per_ml_dominance", axis_name = "Ble Dominance (%)") %>%
  add_row(variable = "Cep_indiv_per_ml_dominance", axis_name = "Cep Dominance (%)") %>%
  add_row(variable = "Col_indiv_per_ml_dominance", axis_name = "Col Dominance (%)") %>%
  add_row(variable = "Eug_indiv_per_ml_dominance", axis_name = "Eug Dominance (%)") %>%
  add_row(variable = "Eup_indiv_per_ml_dominance", axis_name = "Eup Dominance (%)") %>%
  add_row(variable = "Lox_indiv_per_ml_dominance", axis_name = "Lox Dominance (%)") %>%
  add_row(variable = "Pau_indiv_per_ml_dominance", axis_name = "Pau Dominance (%)") %>%
  add_row(variable = "Pca_indiv_per_ml_dominance", axis_name = "Pca Dominance (%)") %>%
  add_row(variable = "Spi_indiv_per_ml_dominance", axis_name = "Spi Dominance (%)") %>%
  add_row(variable = "Spi_te_indiv_per_ml_dominance", axis_name = "Spi te Dominance (%)") %>%
  add_row(variable = "Tet_indiv_per_ml_dominance", axis_name = "Tet Dominance (%)") %>%
  add_row(variable = "Ble_indiv_per_ml_dominance_d", axis_name = "Ble Dominance ES") %>%
  add_row(variable = "Cep_indiv_per_ml_dominance_d", axis_name = "Cep Dominance ES") %>%
  add_row(variable = "Col_indiv_per_ml_dominance_d", axis_name = "Col Dominance ES") %>%
  add_row(variable = "Eug_indiv_per_ml_dominance_d", axis_name = "Eug Dominance ES") %>%
  add_row(variable = "Eup_indiv_per_ml_dominance_d", axis_name = "Eup Dominance ES") %>%
  add_row(variable = "Lox_indiv_per_ml_dominance_d", axis_name = "Lox Dominance ES") %>%
  add_row(variable = "Pau_indiv_per_ml_dominance_d", axis_name = "Pau Dominance ES") %>%
  add_row(variable = "Pca_indiv_per_ml_dominance_d", axis_name = "Pca Dominance ES") %>%
  add_row(variable = "Sp_indiv_per_mli_dominance_d", axis_name = "Spi Dominance ES") %>%
  add_row(variable = "Spi_te_indiv_per_ml_dominance_d", axis_name = "Spi te Dominance ES") %>%
  add_row(variable = "Tet_indiv_per_ml_dominance_d", axis_name = "Tet Dominance ES") %>%
  add_row(variable = "dominance", axis_name = "Dominance (%)") %>%
  add_row(variable = "log_abundance", axis_name = "Log Abundance + 1 (ind/mm²)") %>%
  add_row(variable = "abundance_hedges_d", axis_name = "Density ES") %>%
  add_row(variable = "beta_diversity_from_unconnected", axis_name = "Divergence from unconnected") %>%
  add_row(variable = "beta_diversity_from_previous_time", axis_name = "Temporal Divergence") %>%
  add_row(variable = "beta_diversity_from_previous_time_d", axis_name = "Temporal Divergence ES") %>%
  add_row(variable = "evenness_pielou", axis_name = "Evenness") %>%
  add_row(variable = "evenness_pielou_d", axis_name = "Evenness ES") %>%
  slice(-1)
# --- SET UP COLOUR AND LINE TYPER PER ECOSYSTEM/META-ECOSYSTEM PARAMETERS --- #

treatment_colours = c("Small" = "#feb24c",
                      "Medium" = "#1b7837",
                      "Large" = "#3182bd",
                      "Small-Small" = "#fc9272",
                      "Large-Large" = "#67000d",
                      "Small-Large" = "#762a83",
                      "Medium-Medium" = "#1b7837",
                      "symmetric" = "#1b7837",
                      "asymmetric" = "#762a83")

treatment_colours_paper = c("symmetric" = "#1b7837",
                            "asymmetric" = "#762a83")

treatment_linetype_paper = c("connected" = "solid",
                             "unconnected" = "dashed") 

treatment_linetype = c("connected to small" = "solid",
                       "connected to medium" = "dashed",
                       "connected to large" = "longdash",
                       "connected" = "solid",
                       "unconnected" = "dotted")
# --- SET UP PLOTTING PARAMETERS --- #

figures_height_rmd_output = 7

legend_position = "top"
legend_width_cm = 2
size_legend = 12
size_x_axis = 13
size_y_axis = size_x_axis
boxplot_width = 2
dodging = 0.5 
width_errorbar = 0.2
dodging_error_bar = 0.5

treatment_lines_linewidth = 1
treatment_points_size = 2.5

resource_flow_line_type = "solid"
resource_flow_line_colour = "#d9d9d9"
resource_flow_line_width = 0.3

zero_line_colour = "grey"
zero_line_line_type = "dotted"
zero_line_line_width = 0.5
zero_line_ES_line_type = "dotted"
zero_line_ES_colour = "grey"
zero_line_ES_line_width = 1

ggarrange_margin_top = 0
ggarrange_margin_bottom = 0
ggarrange_margin_left = 0
ggarrange_margin_right = 0

paper_width = 17.3
paper_height = 20
paper_units = "cm"
paper_res = 600
paper_y_axis_size = 9
paper_labels_size = 9

presentation_figure_size = 15
presentation_figure_width = 30
presentation_figure_height = 22
presentation_legend_size = 20
presentation_x_axis_size = 22
presentation_y_axis_size = presentation_x_axis_size
presentation_axes_size = 12
presentation_treatment_points_size = 5
presentation_treatment_linewidth = 2
presentation_figure_units = "cm"
presentation_figure_res = 600

grey_background_xmin = -Inf
grey_background_xmax = 7.5
grey_background_ymin = -Inf
grey_background_ymax = Inf
grey_background_fill = "#f0f0f0"
grey_background_alpha = 0.03
grey_background_color = "transparent"
# --- SET UP MODELLING PARAMETERS --- #

time_point_of_baselines = 1
time_points_with_water_addtion = 3:7
time_points_model = 2:7

Data

Ecosystems information (ecosystems_info)

# --- IMPORT ECOSYSTEM INFORMATION --- #

ecosystems_info = read.csv(here("1_data", "ecosystems_info.csv"), header = TRUE)

Individuals (ds_individuals)

In this dataset (ds_individuals) each row represents an individual at a time point.

# --- IMPORT T0 --- #

# Import the individual data of t0. We considered cultures to be all the same at the beginning (t0). Because of this reason, we filmed only the bottles from which cultures were assembled. Because we want to plot also t0 for the different treatments, we want to assign the video of bottles to all cultures at t0.

ds_individuals_t0_not_elongated = read.csv(here("1_data", 
                                                "individuals_13_threshold", 
                                                "t0.csv")) %>%
  mutate(time_point =  as.numeric(str_extract(time_point, "\\d+")),
         day = 0,
         file =  as.numeric(str_extract(file, "\\d+")),
         video_replicate = file) %>%
  select(time_point,
         day,
         video_replicate,
         file,
         id,
         N_frames,
         mean_area)

# Elongate t0

ds_individuals_t0_elongated = ds_individuals_t0_not_elongated %>%
  map_dfr(.x = 1 : nrow(ecosystems_info),
          .f = ~ ds_individuals_t0_not_elongated) %>% 
  arrange(id) %>% #Id refers to an individual
  mutate(culture_ID = rep(1 : nrow(ecosystems_info),
                          times = nrow(ds_individuals_t0_not_elongated))) %>%
  select(time_point,
         day,
         video_replicate,
         file,
         culture_ID,
         id,
         N_frames,
         mean_area)

expect_equal(nrow(ds_individuals_t0_not_elongated) * nrow(ecosystems_info),
             nrow(ds_individuals_t0_elongated))
# --- IMPORT ALL TIME POINTS BUT T0 --- #

# Set up parameters

ds_individuals_t1_to_t7 = NULL

# Import all time points but t0

for (time_point_i in time_points_without_t0) {
  
  ds_individuals_t1_to_t7[[time_point_i]] = read.csv(here("1_data", 
                                                          "individuals_13_threshold", 
                                                          paste0("t", 
                                                                 time_point_i, 
                                                                 ".csv"))) %>%
    mutate(time_point =  as.numeric(str_extract(time_point, "\\d+")),
           day = time_point_day$day[time_point_day$time_point == time_point_i],
           file =  as.numeric(str_extract(file, "\\d+")),
           video_replicate = ceiling(file/n_cultures)) #Until 110 video replicate = 1, then 2
}

# Tidy up all time points but t0

ds_individuals_t1_to_t7 = ds_individuals_t1_to_t7 %>%
  bind_rows() %>%
  select(time_point,
         day,
         video_replicate,
         file,
         culture_ID,
         id,
         N_frames,
         mean_area)
# --- BIND T0 WITH OTHER TIME POINTS --- #

ds_individuals = rbind(ds_individuals_t0_elongated,
                       ds_individuals_t1_to_t7) %>%
  left_join(ecosystems_info,
            by = "culture_ID") 
# --- RENAME AND SELECT COLUMNS --- #

ds_individuals = ds_individuals %>% 
  rename(ecosystem_size = patch_size,
         ecosystem_size_volume = patch_size_volume) %>%
  select(disturbance,
         disturbance_volume,
         time_point,
         day,
         video_replicate,
         culture_ID,
         system_nr,
         file,
         eco_metaeco_type,
         ecosystem_size,
         ecosystem_size_volume,
         metaecosystem,
         metaecosystem_type,
         mean_area,
         N_frames) %>% 
  rename(ecosystem_size_ml = ecosystem_size_volume,
         ecosystem_type = eco_metaeco_type,
         body_area_µm2 = mean_area)
# --- RENAME AND REORDER LEVELS --- #

ds_individuals <- ds_individuals %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "S" ~ "Small unconnected",
                                    ecosystem_type == "M" ~ "Medium unconnected",
                                    ecosystem_type == "L" ~ "Large unconnected",
                                    ecosystem_type == "S (S_S)" ~ "Small connected to small",
                                    ecosystem_type == "S (S_L)" ~ "Small connected to large",
                                    ecosystem_type == "M (M_M)" ~ "Medium connected to medium",
                                    ecosystem_type == "L (S_L)" ~ "Large connected to small",
                                    ecosystem_type == "L (L_L)" ~ "Large connected to large",
                                    TRUE ~ ecosystem_type), 
         ecosystem_type = factor(ecosystem_type,
                                 levels = ecosystem_types_ordered),
         ecosystem_size = case_when(ecosystem_size == "S" ~ "Small",
                                    ecosystem_size == "M" ~ "Medium",
                                    ecosystem_size == "L" ~ "Large",
                                    TRUE ~ ecosystem_type),
         ecosystem_size = factor(ecosystem_size,
                                 levels = "Small", 
                                 "Medium", 
                                 "Large"),
         size_connected_ecosystem = case_when(ecosystem_type == "Small connected to small" ~ "Small",
                                              ecosystem_type == "Small connected to large" ~ "Large",
                                              ecosystem_type == "Medium connected to medium" ~ "Medium",
                                              ecosystem_type == "Large connected to large" ~ "Large",
                                              ecosystem_type == "Large connected to small" ~ "Small",
                                              TRUE ~ NA_character_))
# --- TAKE OFF PROBLEMATIC VIDEOS --- #

# Set up parameters for testing

ds_individuals_before_taking_off_videos = ds_individuals

# Take off problematic videos

ds_individuals = ds_individuals %>%
  filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))

# Test code

diff = setdiff(ds_individuals_before_taking_off_videos, ds_individuals)
expect_equal(nrow(videos_to_take_off),
             nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))
# --- TAKE OFF PROBLEMATIC ECOSYSTEMS --- #

# Set up parameters for testing

ds_individuals_before_taking_off_cultures = ds_individuals

# Take off problematic ecosystems

ds_individuals = ds_individuals %>%
  filter(!culture_ID %in% ecosystems_to_take_off)

# Test code

expect_equal(setdiff(ds_individuals_before_taking_off_cultures, 
                     ds_individuals) %>% 
               pull(culture_ID) %>% 
               unique(),
             ecosystems_to_take_off)

Patches (ds_ecosystems)

In this dataset (ds_ecosystems) each row represents a ecosystem at a time point. I use the data from the 40 threshold analysis for Ble, Cep, Spi and the data from the 13 threshold analysis for all the other protists (Col, Eup, Lox, Pau, Pca, Spi te, Tet).

# ---  IMPORT & BIND T0 DATASETS --- #

# Import t0

ds_ecosystems_t0 = read.csv(here("1_data", 
                                 "ecosystems_13_threshold", 
                                 "t0.csv")) %>%
  mutate(time_point =  as.numeric(str_extract(time_point, "\\d+")),
         day = 0,
         video_replicate = file) %>%
  select(time_point,
         day,
         video_replicate,
         file,
         bioarea_per_volume,
         indiv_per_volume)

# Describe code

species_ID_13_threshold_t0 = read.csv(here("1_data", 
                                           "species_ID_13_threshold", 
                                           paste0("t0.csv"))) %>%
  rename(Ble_indiv_per_volume = Ble,
         Cep_indiv_per_volume = Cep,
         Col_indiv_per_volume = Col,
         Eug_indiv_per_volume = Eug,
         Eup_indiv_per_volume = Eup,
         Lox_indiv_per_volume = Lox,
         Pau_indiv_per_volume = Pau,
         Pca_indiv_per_volume = Pca,
         Spi_indiv_per_volume = Spi,
         Spi_te_indiv_per_volume = Spi_te,
         Tet_indiv_per_volume = Tet) %>%
  select(file,
         all_of(species_IDD_with_13_threshold_indiv_per_volume))

species_ID_40_threshold_t0 = read.csv(here("1_data", 
                                           "species_ID_40_threshold", 
                                           paste0("t0.csv"))) %>%
  rename(Ble_indiv_per_volume = Ble,
         Cep_indiv_per_volume = Cep,
         Col_indiv_per_volume = Col,
         Eug_indiv_per_volume = Eug,
         Eup_indiv_per_volume = Eup,
         Lox_indiv_per_volume = Lox,
         Pau_indiv_per_volume = Pau,
         Pca_indiv_per_volume = Pca,
         Spi_indiv_per_volume = Spi,
         Spi_te_indiv_per_volume = Spi_te,
         Tet_indiv_per_volume = Tet) %>%
  select(file,
         all_of(species_IDD_with_40_threshold_indiv_per_volume))

# Describe code

ds_ecosystems_t0 = ds_ecosystems_t0 %>%
  left_join(species_ID_13_threshold_t0,
            by = "file") %>%
  left_join(species_ID_40_threshold_t0,
            by = "file") %>%
  mutate(file =  as.numeric(str_extract(file, "\\d+")))
# ---  ELONGATE T0 DATASET --- #

# Set up parameters

ds_ecosystems_t0_elongated <- list()

# Describe code

for (video_i in 1 : n_videos_taken_t0) {
  
  # Describe code

  single_video = ds_ecosystems_t0 %>%
    filter(file == video_i)
  
  # Describe code

  ds_ecosystems_t0_elongated[[video_i]] = ecosystems_info %>%
    mutate(time_point = 0,
           day = 0,
           file = single_video$file,
           video_replicate = single_video$video_replicate,
           bioarea_per_volume = single_video$bioarea_per_volume,
           indiv_per_volume = single_video$indiv_per_volume,
           Ble_indiv_per_volume = single_video$Ble_indiv_per_volume,
           Cep_indiv_per_volume = single_video$Cep_indiv_per_volume,
           Col_indiv_per_volume = single_video$Col_indiv_per_volume,
           Eug_indiv_per_volume = single_video$Eug_indiv_per_volume,
           Eup_indiv_per_volume = single_video$Eup_indiv_per_volume,
           Lox_indiv_per_volume = single_video$Lox_indiv_per_volume,
           Pau_indiv_per_volume = single_video$Pau_indiv_per_volume,
           Pca_indiv_per_volume = single_video$Pca_indiv_per_volume,
           Spi_indiv_per_volume = single_video$Spi_indiv_per_volume,
           Spi_te_indiv_per_volume = single_video$Spi_te_indiv_per_volume,
           Tet_indiv_per_volume = single_video$Tet_indiv_per_volume)
}

# Describe code

ds_ecosystems_t0_elongated = ds_ecosystems_t0_elongated %>%
  bind_rows()
# ---  CLEAN THE COLUMNS OF T0 --- #

ds_ecosystems_t0 = ds_ecosystems_t0_elongated %>%
  select(file,
         time_point,
         day,
         culture_ID,
         video_replicate,
         bioarea_per_volume,
         indiv_per_volume,
         all_of(protist_species_indiv_per_volume))

expect_equal(nrow(ds_ecosystems_t0), 
             sum(n_videos_taken_t0 * n_cultures))
# ---  IMPORT AND BIND ALL TIME POINTS BUT T0 --- #

ds_ecosystems_t1_to_t7 = NULL

for (time_point_i in time_points_without_t0) {
  
  species_ID_13_threshold = read.csv(here("1_data", 
                                          "species_ID_13_threshold", 
                                          paste0("t", time_point_i, ".csv"))) %>%
    rename(Ble_indiv_per_volume = Ble,
           Cep_indiv_per_volume = Cep,
           Col_indiv_per_volume = Col,
           Eug_indiv_per_volume = Eug,
           Eup_indiv_per_volume = Eup,
           Lox_indiv_per_volume = Lox,
           Pau_indiv_per_volume = Pau,
           Pca_indiv_per_volume = Pca,
           Spi_indiv_per_volume = Spi,
           Spi_te_indiv_per_volume = Spi_te,
           Tet_indiv_per_volume = Tet) %>% 
    select(file,
           all_of(species_IDD_with_13_threshold_indiv_per_volume))
  
  
  species_ID_40_threshold = read.csv(here("1_data", 
                                          "species_ID_40_threshold", 
                                          paste0("t", time_point_i, ".csv"))) %>%
    rename(Ble_indiv_per_volume = Ble,
           Cep_indiv_per_volume = Cep,
           Col_indiv_per_volume = Col,
           Eug_indiv_per_volume = Eug,
           Eup_indiv_per_volume = Eup,
           Lox_indiv_per_volume = Lox,
           Pau_indiv_per_volume = Pau,
           Pca_indiv_per_volume = Pca,
           Spi_indiv_per_volume = Spi,
           Spi_te_indiv_per_volume = Spi_te,
           Tet_indiv_per_volume = Tet) %>% 
    select(file,
           all_of(species_IDD_with_40_threshold_indiv_per_volume))
  
  
  ds_ecosystems_t1_to_t7[[time_point_i]] = read.csv(here("1_data", 
                                                      "ecosystems_13_threshold", 
                                                      paste0("t", time_point_i, ".csv"))) %>%
    arrange(file) %>%
    mutate(video_replicate = rep(1 : time_point_day$video_replicates[time_point_i+1],
                                 each = n_cultures),
           day = time_point_day$day[time_point_day$time_point == time_point_i]) %>%
    select(file,
           time_point,
           day,
           video_replicate,
           file,
           culture_ID,
           bioarea_per_volume,
           indiv_per_volume)
  
  ds_ecosystems_t1_to_t7[[time_point_i]] = ds_ecosystems_t1_to_t7[[time_point_i]] %>%
    left_join(species_ID_13_threshold,
                by = "file") %>%
    left_join(species_ID_40_threshold,
                by = "file")
    
}

ds_ecosystems_t1_to_t7 = ds_ecosystems_t1_to_t7 %>%
  bind_rows()
# ---  BIND T0 WITH ALL OTHER TIME POINTS --- #

ds_ecosystems = rbind(ds_ecosystems_t0,
                      ds_ecosystems_t1_to_t7) %>%
  left_join(ecosystems_info,
            by = "culture_ID") 
    
expect_equal(nrow(ds_ecosystems),
             sum(sum(time_point_day$video_replicates) * n_cultures))
# ---  REODER AND RENAME COLUMNS --- #

ds_ecosystems = ds_ecosystems %>%
  rename(ecosystem_size = patch_size,
         ecosystem_size_ml = patch_size_volume) %>%
  select(file,
         time_point,
         day,
         disturbance,
         culture_ID,
         system_nr,
         eco_metaeco_type,
         ecosystem_size,
         ecosystem_size_ml,
         metaecosystem,
         metaecosystem_type,
         video_replicate,
         bioarea_per_volume,
         indiv_per_volume,
         all_of(protist_species_indiv_per_volume)) %>% 
  rename(bioarea_µm2_per_μL = bioarea_per_volume) %>%
  rename_all( ~ gsub("volume", "μL", .))
# ---  RENAME AND REODER LEVELS --- #

ds_ecosystems <- ds_ecosystems %>%
  mutate(ecosystem_size = case_when(ecosystem_size == "S" ~ "Small",
                                    ecosystem_size == "M" ~ "Medium",
                                    ecosystem_size == "L" ~ "Large",
                                    TRUE ~ ecosystem_size), 
         connection = case_when(eco_metaeco_type == "S" ~ "unconnected",
                                     eco_metaeco_type == "M" ~ "unconnected",
                                     eco_metaeco_type == "L" ~ "unconnected",
                                     eco_metaeco_type == "S (S_S)" ~ "connected to small",
                                     eco_metaeco_type == "S (S_L)" ~ "connected to large",
                                     eco_metaeco_type == "M (M_M)" ~ "connected to medium",
                                     eco_metaeco_type == "L (S_L)" ~ "connected to small",
                                     eco_metaeco_type == "L (L_L)" ~ "connected to large"), 
         ecosystem_type = paste(ecosystem_size, connection),
         metaecosystem_type = case_when(metaecosystem_type == "S_S" ~ "Small-Small",
                                        metaecosystem_type == "M_M" ~ "Medium-Medium",
                                        metaecosystem_type == "L_L" ~ "Large-Large",
                                        metaecosystem_type == "S_L" ~ "Small-Large",
                                        TRUE ~ metaecosystem_type),
    time_point =  as.numeric(str_extract(time_point, "\\d+")),
    file =  as.numeric(str_extract(file, "\\d+")))
# ---  CHANGE UNITS OF MEASUREMENTS TO ML --- #

ds_ecosystems = ds_ecosystems %>%
  mutate(bioarea_µm2_per_ml = bioarea_µm2_per_μL * 10^3,
         bioarea_mm2_per_ml = bioarea_µm2_per_ml * 10^(-6),
         Ble_indiv_per_ml = Ble_indiv_per_μL * 10^3,
         Cep_indiv_per_ml = Cep_indiv_per_μL * 10^3,
         Col_indiv_per_ml = Col_indiv_per_μL * 10^3,
         Eug_indiv_per_ml = Eug_indiv_per_μL * 10^3,
         Eup_indiv_per_ml = Eup_indiv_per_μL * 10^3,
         Lox_indiv_per_ml = Lox_indiv_per_μL * 10^3,
         Pau_indiv_per_ml = Pau_indiv_per_μL * 10^3,
         Pca_indiv_per_ml = Pca_indiv_per_μL * 10^3,
         Spi_indiv_per_ml = Spi_indiv_per_μL * 10^3,
         Spi_te_indiv_per_ml = Spi_te_indiv_per_μL * 10^3,
         Tet_indiv_per_ml = Tet_indiv_per_μL * 10^3)
# ---  TAKE OFF PROBLEMATIC VIDEOS --- #

# Set up parameters

ds_ecosystems_before_taking_off_videos = ds_ecosystems

# Take off problematic videos

ds_ecosystems = ds_ecosystems %>%
  filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))

# Test code

diff = setdiff(ds_ecosystems_before_taking_off_videos, ds_ecosystems)
expect_equal(nrow(videos_to_take_off),
             nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))
# ---  TAKE OFF PROBLEMATIC ECOSYSTEMS --- #

# Set up parameters

ds_ecosystems_before_taking_off_cultures = ds_ecosystems

# Take off problematic ecosystems

ds_ecosystems = ds_ecosystems %>%
  filter(!culture_ID %in% ecosystems_to_take_off)

# Test code

expect_equal(setdiff(ds_ecosystems_before_taking_off_cultures, 
                     ds_ecosystems) %>% 
               pull(culture_ID) %>% 
               unique(),
             ecosystems_to_take_off)
# ---  AVERAGE VIDEOS --- #

# Average videos

ds_ecosystems = ds_ecosystems %>%
  group_by(across(all_of(columns_ecosystems))) %>%
  summarise(across(contains("_per_ml"), mean),
            across(contains("_tot"), mean)) %>%
  ungroup()

# Test code

expect_equal(nrow(ds_ecosystems), 
             (n_cultures - length(ecosystems_to_take_off)) * length(time_points))
# ---  ADD CONNECTION AND INDIVIDUALS --- #

ds_ecosystems = ds_ecosystems %>%
  mutate(indiv_per_ml = !!rlang::parse_expr(paste(protist_species_indiv_per_ml, 
                                                  collapse = " + ")))
# --- CALCULATE TOTAL RESPONSE VARIABLE FOR THE WHOLE ECOSYSTEM --- #

ds_ecosystems = ds_ecosystems %>%
  mutate(bioarea_tot_mm2 = bioarea_mm2_per_ml * ecosystem_size_ml,
         indiv_tot = indiv_per_ml * ecosystem_size_ml,
         Ble_tot_indiv = Ble_indiv_per_ml * ecosystem_size_ml,
         Cep_tot_indiv = Cep_indiv_per_ml * ecosystem_size_ml,
         Col_tot_indiv = Col_indiv_per_ml * ecosystem_size_ml,
         Eug_tot_indiv = Eug_indiv_per_ml * ecosystem_size_ml,
         Eup_tot_indiv = Eup_indiv_per_ml * ecosystem_size_ml,
         Lox_tot_indiv = Lox_indiv_per_ml * ecosystem_size_ml,
         Pau_tot_indiv = Pau_indiv_per_ml * ecosystem_size_ml,
         Pca_tot_indiv = Pca_indiv_per_ml * ecosystem_size_ml,
         Spi_tot_indiv = Spi_indiv_per_ml * ecosystem_size_ml,
         Spi_te_tot_indiv = Spi_te_indiv_per_ml * ecosystem_size_ml,
         Tet_tot_indiv = Tet_indiv_per_ml * ecosystem_size_ml)
# ---  CALCULATE SPECIES DOMINANCE --- #

# Calculate species dominance

ds_ecosystems = ds_ecosystems %>%
  mutate(across(.cols = all_of(protist_species_indiv_per_ml), 
                .fns = list(dominance = ~ (. / indiv_per_ml) * 100), 
                .names = "{col}_dominance"))

# Test code

expect_equal(unique(ds_ecosystems$Ble_indiv_per_ml_dominance[ds_ecosystems$indiv_per_ml == 0]), NaN)
if (FALSE %in% unique((ds_ecosystems$Ble_indiv_per_ml/ds_ecosystems$indiv_per_ml) *100 == ds_ecosystems$Ble_indiv_per_ml_dominance)) stop()
# ---  CALCULATE ALPHA DIVERSITY (SHANNON, SIMPSON, INVERSE SIMPSON, EVENNESS) --- #

# Set up parameters for testing

n_rows_ds_ecosystems_before_calculating_alpha = nrow(ds_ecosystems)

# Calculate alpha diversity

ds_ecosystems = calculate.alpha.diversity()

# Test code

expect_equal(max(ds_ecosystems$species_richness), 
             length(protist_species))

expect_equal(nrow(ds_ecosystems),
             n_rows_ds_ecosystems_before_calculating_alpha)
# ---  CALCULATE MEDIAN BODY SIZE --- #

# Set up parameters for testing

n_rows_ds_ecosystems_before_median_size = nrow(ds_ecosystems)

# Calculate median body size

ds_median_body_size = ds_individuals %>%
  group_by(time_point,
           culture_ID,
           file) %>%
  summarise(median_body_area_µm2 = median(body_area_µm2)) %>%
  group_by(time_point,
           culture_ID) %>%
  summarise(median_body_area_µm2 = mean(median_body_area_µm2))

# Test code

expect_true(nrow(ds_median_body_size) <= nrow(ds_ecosystems)) #Ds median body size could be less because some cultures might be crashed and not have any individual.

# Set up parameters for testing

ds_ecosystems_before_full_join = ds_ecosystems

# Join the median body size with ds_ecosystems

ds_ecosystems = full_join(ds_ecosystems, ds_median_body_size)

# Test code

expect_equal(nrow(ds_ecosystems), 
             n_rows_ds_ecosystems_before_median_size)
# --- CALCULATE AUTO/HETEROTROPHIC RATIO --- #

ds_ecosystems = ds_ecosystems %>%
  mutate(auto_hetero_ratio = (Eug_indiv_per_ml + Eup_indiv_per_ml) / 
                             (Ble_indiv_per_ml + 
                              Cep_indiv_per_ml + 
                              Col_indiv_per_ml + 
                              Lox_indiv_per_ml + 
                              Pau_indiv_per_ml + 
                              Pca_indiv_per_ml +
                              Spi_indiv_per_ml + 
                              Spi_te_indiv_per_ml +
                              Tet_indiv_per_ml))
# --- ADD EVAPORATION RATES --- #

# Manipulate evaporation rates data

ds_for_evaporation = read.csv(here("1_data", 
                                   "evaporation", 
                                   "water_addition.csv")) %>%
  pivot_longer(cols = starts_with("water_add_after_t"), 
               names_to = "time_point",          
               values_to = "water_addition_ml") %>%
  mutate(time_point = as.double(str_extract(time_point, "\\d+")) + 1)

# Add evaporation rates to ds_ecosystems

ds_ecosystems = ds_ecosystems %>%
  left_join(ds_for_evaporation)
# --- ADD TRANSFORMED VARIABLES --- #

ds_ecosystems = ds_ecosystems %>%
  mutate(sqrt_bioarea_mm2_per_ml = sqrt(bioarea_mm2_per_ml),
         sqrt_auto_hetero_ratio = sqrt(auto_hetero_ratio))

Patch effect sizes (ds_ecosystems_effect_size)

In this dataset (ds_ecosystems_effect_size) each row represents a treatment at a time point. It contains the effect size of the connection of a ecosystem (connected vs unconnected).

# ---  CALCULATE THE MEAN & SD OF RESPONSE VARIABLES FOR EACH TREATMENT/CONTROL AT EACH TIME POINT --- #

ds_ecosystems_effect_size = NULL
variable_nr = 0

for (variable_i in variables_ecosystems) {
  
  variable_nr = variable_nr + 1
  
  ds_ecosystems_effect_size[[variable_nr]] = ds_ecosystems %>%
    filter(time_point >= 1,
           !is.na(!!sym(variable_i))) %>%
    group_by(across(all_of(columns_ecosystems[columns_ecosystems != "culture_ID" & 
                                           columns_ecosystems != "system_nr"]))) %>%
    summarise(across(all_of(variable_i),
                     list(mean = mean,
                          sd = sd)),
              sample_size = n()) %>%
    rename_with( ~ paste0(variable_i, "_sample_size"),
                 matches("sample_size"))
  
}

ds_ecosystems_effect_size <- reduce(ds_ecosystems_effect_size,
                                    full_join,
                                    by = columns_ecosystems[columns_ecosystems != "culture_ID" & columns_ecosystems != "system_nr"])

expect_equal(nrow(ds_ecosystems_effect_size),
             n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)
# --- CALCULATE THE EFFECT SIZE (HEDGE'S D) FOR EACH TREATMENT AT EACH TIME POINT --- #
  
  for (variable_i in variables_ecosystems) {
    ds_ecosystems_effect_size <- ds_ecosystems_effect_size %>%
      mutate(!!paste0(variable_i, "_d") := NA,
             !!paste0(variable_i, "_d_upper") := NA,
             !!paste0(variable_i, "_d_lower") := NA)
  }
  
  row_i = 0
  for (treatment_selected in treatments_and_controls$treatment) {
    for (time_point_selected in time_points) {
      
      row_i = row_i + 1
      
      control_input = treatments_and_controls$control[treatments_and_controls$treatment == treatment_selected]
      
      treatment_row = ds_ecosystems_effect_size %>%
        filter(ecosystem_type == treatment_selected,
               time_point == time_point_selected)
      
      control_row = ds_ecosystems_effect_size %>%
        filter(ecosystem_type == control_input,
               time_point == time_point_selected)
      
      for (response_variable in variables_ecosystems) {
        
        hedges_d = calculate.hedges_d(treatment_row[[paste0(response_variable, "_mean")]],
                                      treatment_row[[paste0(response_variable, "_sd")]],
                                      treatment_row[[paste0(response_variable, "_sample_size")]],
                                      control_row[[paste0(response_variable, "_mean")]],
                                      control_row[[paste0(response_variable, "_sd")]],
                                      control_row[[paste0(response_variable, "_sample_size")]])
        
        ds_ecosystems_effect_size[[paste0(response_variable, "_d")]][
          ds_ecosystems_effect_size$ecosystem_type == treatment_selected &
          ds_ecosystems_effect_size$time_point == time_point_selected] =
          hedges_d$d
        
        ds_ecosystems_effect_size[[paste0(response_variable, "_d_upper")]][
          ds_ecosystems_effect_size$ecosystem_type == treatment_selected &
          ds_ecosystems_effect_size$time_point == time_point_selected] =
          hedges_d$upper_CI
        
        ds_ecosystems_effect_size[[paste0(response_variable, "_d_lower")]][
          ds_ecosystems_effect_size$ecosystem_type == treatment_selected &
          ds_ecosystems_effect_size$time_point == time_point_selected] =
          hedges_d$lower_CI
        
      }
    }
  }

expect_equal(nrow(ds_ecosystems_effect_size),
             n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)

Meta-ecosystems (ds_metaecosystems)

In this dataset (ds_metaecosystems) each row represents a meta-ecosystem or a two-ecosystem unconnected system at a time point.

# --- FIND IDS OF UNCONNECTED ECOSYSTEMS --- #

ID_unconnected_S_low = ds_ecosystems %>%
  filter(ecosystem_type == "Small unconnected",
         disturbance == "low") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_M_low = ds_ecosystems %>%
  filter(ecosystem_type == "Medium unconnected",
         disturbance == "low") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_L_low = ds_ecosystems %>%
  filter(ecosystem_type == "Large unconnected",
         disturbance == "low") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_S_high = ds_ecosystems %>%
  filter(ecosystem_type == "Small unconnected",
         disturbance == "high") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_M_high = ds_ecosystems %>%
  filter(ecosystem_type == "Medium unconnected",
         disturbance == "high") %>%
  pull(culture_ID) %>%
  unique()

ID_unconnected_L_high = ds_ecosystems %>%
  filter(ecosystem_type == "Large unconnected",
         disturbance == "high") %>%
  pull(culture_ID) %>%
  unique()
# --- FIND COMBINATIONS OF ECOSYSTEMS TO CREATE UNCONNECTED META-ECOSYSTEMS --- #

combinations_S_and_L_low = crossing(ID_unconnected_S_low,
                                    ID_unconnected_L_low) %>%
                            mutate(disturbance = "low",
                                   metaecosystem_type = "Small-Large",
                                   connection = "unconnected") %>%
                            rename(ID_first_ecosystem = ID_unconnected_S_low,
                                   ID_second_ecosystem = ID_unconnected_L_low) %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   connection,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)

combinations_S_and_L_high = crossing(ID_unconnected_S_high,
                                     ID_unconnected_L_high) %>%
                            mutate(disturbance = "high",
                                   metaecosystem_type = "Small-Large",
                                   connection = "unconnected") %>%
                            rename(ID_first_ecosystem = ID_unconnected_S_high,
                                   ID_second_ecosystem = ID_unconnected_L_high) %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   connection,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)

combinations_M_and_M_low = combinat::combn(ID_unconnected_M_low,
                                           m = 2) %>%
                            t() %>%
                            as.data.frame() %>%
                            rename(ID_first_ecosystem = V1,
                                   ID_second_ecosystem = V2) %>%
                            mutate(disturbance = "low",
                                   metaecosystem_type = "Medium-Medium",
                                   connection = "unconnected") %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   connection,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)

combinations_M_and_M_high = combinat::combn(ID_unconnected_M_high,
                                            m = 2) %>%
                            t() %>%
                            as.data.frame() %>%
                            rename(ID_first_ecosystem = V1,
                                   ID_second_ecosystem = V2) %>%
                            mutate(disturbance = "high",
                                   metaecosystem_type = "Medium-Medium",
                                   connection = "unconnected") %>%
                            select(disturbance,
                                   metaecosystem_type,
                                   connection,
                                   ID_first_ecosystem,
                                   ID_second_ecosystem)
# --- BIND ECOSYSTEM COMBINATIONS --- #

combinations_unconnected_metaeco = rbind(combinations_S_and_L_low,
                                         combinations_S_and_L_high,
                                         combinations_M_and_M_low,
                                         combinations_M_and_M_high) %>% 
  mutate(system_nr = 1001:(1000 + nrow(.))) %>%
  select(system_nr,
         disturbance,
         metaecosystem_type,
         connection,
         ID_first_ecosystem,
         ID_second_ecosystem)
# --- FIND COMBINATIONS OF ECOSYSTEMS TO CREATE CONNECTED META-ECOSYSTEMS --- #

combinations_connected_metaeco = ds_ecosystems %>%
  filter(time_point == 0,
         metaecosystem == "yes") %>%
  select(system_nr,
         disturbance,
         metaecosystem_type,
         culture_ID) %>%
  group_by(system_nr,
           disturbance,
           metaecosystem_type) %>%
  summarise(ID_first_ecosystem = (mean(culture_ID) - 0.5),
            ID_second_ecosystem = (mean(culture_ID) + 0.5)) %>%
  mutate(connection = "connected") %>%
  as.data.frame()
# --- BIND COMBINATIONS OF ECOSYSTEMS TO CREATE UNCONNECTED & CONNECTED META-ECOSYSTEMS --- #

ecos_combin = rbind(combinations_unconnected_metaeco,
                               combinations_connected_metaeco) %>%
  mutate(ecosystems_combined = paste0(ID_first_ecosystem, "|", ID_second_ecosystem))

n_ecosystems_combinations = nrow(ecos_combin)
# --- CREATE SETS FOR SMALL-LARGE UNCONNECTED META-ECOSYSTEMS --- #

# Create sets for Small-Large unconnected meta-ecosystems where in each set a small and a large ecosystems are paired differently (keep the small ecosystems on the same order and perform permutations on the large ecosystems)

SL_unconn_ecos_comb_sets <- vector("list",
                                  length(disturbance_levels))

for (disturbance_i in 1:length(disturbance_levels)) {
  
  ID_small_ecosystems = ds_ecosystems %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           ecosystem_type == "Small unconnected") %>%
    pull(culture_ID) %>%
    unique()
  
  ID_large_ecosystems = ds_ecosystems %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           ecosystem_type == "Large unconnected") %>%
    pull(culture_ID) %>%
    unique()
  
  #Force small and large ecosystems vectors to have the same length
  
  length_difference <- length(ID_small_ecosystems) - length(ID_large_ecosystems)
  
  if (length_difference > 0) {
    
    ID_large_ecosystems = c(ID_large_ecosystems,
                       rep("Patch taken off",
                           times = abs(length(ID_small_ecosystems) - 
                                       length(ID_large_ecosystems))))
    
    } else if (length_difference < 0) {
      
    ID_small_ecosystems = c(ID_small_ecosystems,
                         rep("Patch taken off",
                             times = abs(length(ID_large_ecosystems) - 
                                         length(ID_small_ecosystems))))
    }

  # Create dataframe
  
  permutations_large = permn(ID_large_ecosystems)
  
  SL_unconn_ecos_comb_sets[[disturbance_i]] = data.frame(
    disturbance = disturbance_levels[disturbance_i],
    metaecosystem_type = "Small-Large",
    connection = "unconnected",
    ID_first_ecosystem = rep(ID_small_ecosystems, 
                             times = length(permutations_large)),
    ID_second_ecosystem = unlist(permutations_large),
    set = rep(1 : length(permutations_large), 
              each = length(ID_small_ecosystems)))
  
  expect_equal(nrow(SL_unconn_ecos_comb_sets[[disturbance_i]]),
               length(ID_small_ecosystems) * length(permutations_large))
  
  SL_unconn_ecos_comb_sets[[disturbance_i]] = SL_unconn_ecos_comb_sets[[disturbance_i]] %>%
    filter(!ID_first_ecosystem == "Patch taken off",
           !ID_second_ecosystem == "Patch taken off") %>%
    mutate(ID_first_ecosystem = as.double(ID_first_ecosystem),
           ID_second_ecosystem = as.double(ID_second_ecosystem)) %>%
    full_join(ecos_combin %>%
                filter(disturbance == disturbance_levels[disturbance_i], 
                       metaecosystem_type == "Small-Large",
                       connection == "unconnected")) #Add system_nr & ecosystems_combined

}

SL_unconn_ecos_comb_sets_before_binding = SL_unconn_ecos_comb_sets
SL_unconn_ecos_comb_sets = SL_unconn_ecos_comb_sets %>%
  bind_rows()
# --- TEST CODE --- #

expect_equal(nrow(SL_unconn_ecos_comb_sets),
             nrow(SL_unconn_ecos_comb_sets_before_binding[[1]]) + nrow(SL_unconn_ecos_comb_sets_before_binding[[2]]))

expect_equal(length(SL_unconn_ecos_comb_sets %>% 
                      pull(system_nr) %>% 
                      unique()),
             length(ecos_combin %>%
                      filter(metaecosystem_type == "Small-Large",
                             connection == "unconnected") %>%
                      pull(system_nr) %>%
                      unique()))
# --- CREATE SETS FOR MEDIUM-MEDIUM UNCONNECTED META-ECOSYSTEMS --- #

# Create sets for Medium-Medium unconnected meta-ecosystems where in each set two different medium ecosystems are paired. To do so, initialise MM_unconn_ecos_comb_sets. Assign 10^4 rows to each matrix so that we have enough rows not to run out of them when we try to assign values to them. Assign 4 columns which will include culture_ID of the first system, second culture_ID of the fist system, culture_ID of the second system, and second culture_ID of the second system.  

MM_unconn_ecos_comb_sets = NULL
for(disturbance_i in 1:length(disturbance_levels)){
  
  MM_unconn_ecos_comb_sets[[disturbance_i]] <- matrix(nrow = 10 ^ 4, 
                                                 ncol = 4)
  
}

for (disturbance_i in 1:length(disturbance_levels)) {
  
  ID_medium_ecosystems = ds_ecosystems %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           ecosystem_type == "Medium unconnected") %>%
    pull(culture_ID) %>%
    unique()
  
  MM_unconnected_systems = combn(ID_medium_ecosystems, 
                              2) %>%
    t()
  
  matrix_row = 0
  for (first_system_i in 1:nrow(MM_unconnected_systems)) {
    
    #Find culture IDs of the first system (what's the first system?)
    first_system = MM_unconnected_systems[first_system_i, ]
    
    for (second_system_i in 1:nrow(MM_unconnected_systems)) {
      
      #Find culture IDs of the second system (what's the second system?)
      second_system = MM_unconnected_systems[second_system_i, ]
      
      shared_elements_among_systems = intersect(first_system,
                                                second_system)
      
      if (length(shared_elements_among_systems) == 0) {
        
        matrix_row = matrix_row + 1
        
        #Make first and second system into a set
        MM_unconn_ecos_comb_sets[[disturbance_i]][matrix_row,] = c(first_system,
                                                            second_system)
        
        print(MM_unconn_ecos_comb_sets[[disturbance_i]][matrix_row,])
        
      }
    }
  }
  
  #Tidy the dataset with all the ecosystem combinations
  
  MM_unconn_ecos_comb_sets[[disturbance_i]] = MM_unconn_ecos_comb_sets[[disturbance_i]] %>%
    as.data.frame() %>%
    drop_na()
  
  # Test code
  
  expect_equal(MM_unconn_ecos_comb_sets[[disturbance_i]] %>% 
                 filter(V1 == V2 | 
                        V1 == V3 | 
                        V1 == V4 | 
                        V2 == V3 | 
                        V2 == V4 | 
                        V3 == V4) %>% 
                 nrow(),
               0)
  
  #Reorder the dataset with all the ecosystem combinations
  
  MM_unconn_ecos_comb_sets_reordered = data.frame(ID_first_ecosystem = NA,
                                          ID_second_ecosystem = NA,
                                          set = NA)
  
  for (set_input in 1:nrow(MM_unconn_ecos_comb_sets[[disturbance_i]])) {
    MM_unconn_ecos_comb_sets_reordered = MM_unconn_ecos_comb_sets_reordered %>%
      add_row(ID_first_ecosystem = MM_unconn_ecos_comb_sets[[disturbance_i]][set_input, 1],
              ID_second_ecosystem = MM_unconn_ecos_comb_sets[[disturbance_i]][set_input, 2],
              set = set_input) %>%
      add_row(ID_first_ecosystem = MM_unconn_ecos_comb_sets[[disturbance_i]][set_input, 3],
              ID_second_ecosystem = MM_unconn_ecos_comb_sets[[disturbance_i]][set_input, 4],
              set = set_input)
  }
  
  #Add to a list
  
  MM_unconn_ecos_comb_sets[[disturbance_i]] = MM_unconn_ecos_comb_sets_reordered %>%
    drop_na() %>%
    mutate(disturbance = disturbance_levels[disturbance_i],
           metaecosystem_type = "Medium-Medium",
           connection = "unconnected")
  
  #Add system nr
  
  ID_combinations_MM_unconnected = ecos_combin %>%
    filter(disturbance == disturbance_levels[disturbance_i],
           metaecosystem_type == "Medium-Medium",
           connection == "unconnected")
  
  MM_unconn_ecos_comb_sets[[disturbance_i]] = full_join(MM_unconn_ecos_comb_sets[[disturbance_i]],
                                                   ID_combinations_MM_unconnected)
  
}
## [1] 6 7 8 9
## [1]  6  7  8 10
## [1]  6  7  9 10
## [1] 6 8 7 9
## [1]  6  8  7 10
## [1]  6  8  9 10
## [1] 6 9 7 8
## [1]  6  9  7 10
## [1]  6  9  8 10
## [1]  6 10  7  8
## [1]  6 10  7  9
## [1]  6 10  8  9
## [1] 7 8 6 9
## [1]  7  8  6 10
## [1]  7  8  9 10
## [1] 7 9 6 8
## [1]  7  9  6 10
## [1]  7  9  8 10
## [1]  7 10  6  8
## [1]  7 10  6  9
## [1]  7 10  8  9
## [1] 8 9 6 7
## [1]  8  9  6 10
## [1]  8  9  7 10
## [1]  8 10  6  7
## [1]  8 10  6  9
## [1]  8 10  7  9
## [1]  9 10  6  7
## [1]  9 10  6  8
## [1]  9 10  7  8
## [1] 61 62 63 64
## [1] 61 62 63 65
## [1] 61 62 64 65
## [1] 61 63 62 64
## [1] 61 63 62 65
## [1] 61 63 64 65
## [1] 61 64 62 63
## [1] 61 64 62 65
## [1] 61 64 63 65
## [1] 61 65 62 63
## [1] 61 65 62 64
## [1] 61 65 63 64
## [1] 62 63 61 64
## [1] 62 63 61 65
## [1] 62 63 64 65
## [1] 62 64 61 63
## [1] 62 64 61 65
## [1] 62 64 63 65
## [1] 62 65 61 63
## [1] 62 65 61 64
## [1] 62 65 63 64
## [1] 63 64 61 62
## [1] 63 64 61 65
## [1] 63 64 62 65
## [1] 63 65 61 62
## [1] 63 65 61 64
## [1] 63 65 62 64
## [1] 64 65 61 62
## [1] 64 65 61 63
## [1] 64 65 62 63
#Bind all sets of MM unconnected

MM_unconn_ecos_comb_sets = MM_unconn_ecos_comb_sets %>%
  bind_rows()
# --- TEST CODE --- #

expect_equal(length(MM_unconn_ecos_comb_sets %>%
                      pull(system_nr) %>%
                      unique()),
             length(ecos_combin %>%
                      filter(metaecosystem_type == "Medium-Medium",
                             connection == "unconnected") %>%
                      pull(system_nr) %>%
                      unique()))
# --- BIND SL AND MM UNCONNECTED META-ECOSYSTEMS SETS --- #

ecos_combin_unconn_sets = rbind(SL_unconn_ecos_comb_sets, 
                                MM_unconn_ecos_comb_sets) %>%
  select(disturbance,
         metaecosystem_type,
         connection,
         set,
         system_nr,
         ID_first_ecosystem,
         ID_second_ecosystem)
# --- FIND SETS OF SETS --- #

# Find the number of combinations of SL & MM low or high disturbance

n_SL_low_sets = ecos_combin_unconn_sets %>%
  filter(metaecosystem_type == "Small-Large",
         disturbance == "low") %>%
  pull(set) %>%
  max()

n_SL_high_sets = ecos_combin_unconn_sets %>%
  filter(metaecosystem_type == "Small-Large",
         disturbance == "high") %>%
  pull(set) %>%
  max()

n_MM_low_sets = ecos_combin_unconn_sets %>%
  filter(metaecosystem_type == "Medium-Medium",
         disturbance == "low") %>%
  pull(set) %>%
  max()

n_MM_high_sets = ecos_combin_unconn_sets %>%
  filter(metaecosystem_type == "Medium-Medium",
         disturbance == "high") %>%
  pull(set) %>%
  max()

# Find combinations of sets

ecos_combin_unconn_sets_of_sets <- expand.grid(set_SL_low = 1:n_SL_low_sets,
                                            set_SL_high = 1:n_SL_high_sets,
                                            set_MM_low = 1:n_MM_low_sets,
                                            set_MM_high = 1:n_MM_high_sets) %>%
  print()
##       set_SL_low set_SL_high set_MM_low set_MM_high
## 1              1           1          1           1
## 2              2           1          1           1
## 3              3           1          1           1
## 4              4           1          1           1
## 5              5           1          1           1
## 6              6           1          1           1
## 7              7           1          1           1
## 8              8           1          1           1
## 9              9           1          1           1
## 10            10           1          1           1
## 11            11           1          1           1
## 12            12           1          1           1
## 13            13           1          1           1
## 14            14           1          1           1
## 15            15           1          1           1
## 16            16           1          1           1
## 17            17           1          1           1
## 18            18           1          1           1
## 19            19           1          1           1
## 20            20           1          1           1
## 21            21           1          1           1
## 22            22           1          1           1
## 23            23           1          1           1
## 24            24           1          1           1
## 25            25           1          1           1
## 26            26           1          1           1
## 27            27           1          1           1
## 28            28           1          1           1
## 29            29           1          1           1
## 30            30           1          1           1
## 31            31           1          1           1
## 32            32           1          1           1
## 33            33           1          1           1
## 34            34           1          1           1
## 35            35           1          1           1
## 36            36           1          1           1
## 37            37           1          1           1
## 38            38           1          1           1
## 39            39           1          1           1
## 40            40           1          1           1
## 41            41           1          1           1
## 42            42           1          1           1
## 43            43           1          1           1
## 44            44           1          1           1
## 45            45           1          1           1
## 46            46           1          1           1
## 47            47           1          1           1
## 48            48           1          1           1
## 49            49           1          1           1
## 50            50           1          1           1
## 51            51           1          1           1
## 52            52           1          1           1
## 53            53           1          1           1
## 54            54           1          1           1
## 55            55           1          1           1
## 56            56           1          1           1
## 57            57           1          1           1
## 58            58           1          1           1
## 59            59           1          1           1
## 60            60           1          1           1
## 61            61           1          1           1
## 62            62           1          1           1
## 63            63           1          1           1
## 64            64           1          1           1
## 65            65           1          1           1
## 66            66           1          1           1
## 67            67           1          1           1
## 68            68           1          1           1
## 69            69           1          1           1
## 70            70           1          1           1
## 71            71           1          1           1
## 72            72           1          1           1
## 73            73           1          1           1
## 74            74           1          1           1
## 75            75           1          1           1
## 76            76           1          1           1
## 77            77           1          1           1
## 78            78           1          1           1
## 79            79           1          1           1
## 80            80           1          1           1
## 81            81           1          1           1
## 82            82           1          1           1
## 83            83           1          1           1
## 84            84           1          1           1
## 85            85           1          1           1
## 86            86           1          1           1
## 87            87           1          1           1
## 88            88           1          1           1
## 89            89           1          1           1
## 90            90           1          1           1
## 91            91           1          1           1
## 92            92           1          1           1
## 93            93           1          1           1
## 94            94           1          1           1
## 95            95           1          1           1
## 96            96           1          1           1
## 97            97           1          1           1
## 98            98           1          1           1
## 99            99           1          1           1
## 100          100           1          1           1
## 101          101           1          1           1
## 102          102           1          1           1
## 103          103           1          1           1
## 104          104           1          1           1
## 105          105           1          1           1
## 106          106           1          1           1
## 107          107           1          1           1
## 108          108           1          1           1
## 109          109           1          1           1
## 110          110           1          1           1
## 111          111           1          1           1
## 112          112           1          1           1
## 113          113           1          1           1
## 114          114           1          1           1
## 115          115           1          1           1
## 116          116           1          1           1
## 117          117           1          1           1
## 118          118           1          1           1
## 119          119           1          1           1
## 120          120           1          1           1
## 121            1           2          1           1
## 122            2           2          1           1
## 123            3           2          1           1
## 124            4           2          1           1
## 125            5           2          1           1
## 126            6           2          1           1
## 127            7           2          1           1
## 128            8           2          1           1
## 129            9           2          1           1
## 130           10           2          1           1
## 131           11           2          1           1
## 132           12           2          1           1
## 133           13           2          1           1
## 134           14           2          1           1
## 135           15           2          1           1
## 136           16           2          1           1
## 137           17           2          1           1
## 138           18           2          1           1
## 139           19           2          1           1
## 140           20           2          1           1
## 141           21           2          1           1
## 142           22           2          1           1
## 143           23           2          1           1
## 144           24           2          1           1
## 145           25           2          1           1
## 146           26           2          1           1
## 147           27           2          1           1
## 148           28           2          1           1
## 149           29           2          1           1
## 150           30           2          1           1
## 151           31           2          1           1
## 152           32           2          1           1
## 153           33           2          1           1
## 154           34           2          1           1
## 155           35           2          1           1
## 156           36           2          1           1
## 157           37           2          1           1
## 158           38           2          1           1
## 159           39           2          1           1
## 160           40           2          1           1
## 161           41           2          1           1
## 162           42           2          1           1
## 163           43           2          1           1
## 164           44           2          1           1
## 165           45           2          1           1
## 166           46           2          1           1
## 167           47           2          1           1
## 168           48           2          1           1
## 169           49           2          1           1
## 170           50           2          1           1
## 171           51           2          1           1
## 172           52           2          1           1
## 173           53           2          1           1
## 174           54           2          1           1
## 175           55           2          1           1
## 176           56           2          1           1
## 177           57           2          1           1
## 178           58           2          1           1
## 179           59           2          1           1
## 180           60           2          1           1
## 181           61           2          1           1
## 182           62           2          1           1
## 183           63           2          1           1
## 184           64           2          1           1
## 185           65           2          1           1
## 186           66           2          1           1
## 187           67           2          1           1
## 188           68           2          1           1
## 189           69           2          1           1
## 190           70           2          1           1
## 191           71           2          1           1
## 192           72           2          1           1
## 193           73           2          1           1
## 194           74           2          1           1
## 195           75           2          1           1
## 196           76           2          1           1
## 197           77           2          1           1
## 198           78           2          1           1
## 199           79           2          1           1
## 200           80           2          1           1
## 201           81           2          1           1
## 202           82           2          1           1
## 203           83           2          1           1
## 204           84           2          1           1
## 205           85           2          1           1
## 206           86           2          1           1
## 207           87           2          1           1
## 208           88           2          1           1
## 209           89           2          1           1
## 210           90           2          1           1
## 211           91           2          1           1
## 212           92           2          1           1
## 213           93           2          1           1
## 214           94           2          1           1
## 215           95           2          1           1
## 216           96           2          1           1
## 217           97           2          1           1
## 218           98           2          1           1
## 219           99           2          1           1
## 220          100           2          1           1
## 221          101           2          1           1
## 222          102           2          1           1
## 223          103           2          1           1
## 224          104           2          1           1
## 225          105           2          1           1
## 226          106           2          1           1
## 227          107           2          1           1
## 228          108           2          1           1
## 229          109           2          1           1
## 230          110           2          1           1
## 231          111           2          1           1
## 232          112           2          1           1
## 233          113           2          1           1
## 234          114           2          1           1
## 235          115           2          1           1
## 236          116           2          1           1
## 237          117           2          1           1
## 238          118           2          1           1
## 239          119           2          1           1
## 240          120           2          1           1
## 241            1           3          1           1
## 242            2           3          1           1
## 243            3           3          1           1
## 244            4           3          1           1
## 245            5           3          1           1
## 246            6           3          1           1
## 247            7           3          1           1
## 248            8           3          1           1
## 249            9           3          1           1
## 250           10           3          1           1
## 251           11           3          1           1
## 252           12           3          1           1
## 253           13           3          1           1
## 254           14           3          1           1
## 255           15           3          1           1
## 256           16           3          1           1
## 257           17           3          1           1
## 258           18           3          1           1
## 259           19           3          1           1
## 260           20           3          1           1
## 261           21           3          1           1
## 262           22           3          1           1
## 263           23           3          1           1
## 264           24           3          1           1
## 265           25           3          1           1
## 266           26           3          1           1
## 267           27           3          1           1
## 268           28           3          1           1
## 269           29           3          1           1
## 270           30           3          1           1
## 271           31           3          1           1
## 272           32           3          1           1
## 273           33           3          1           1
## 274           34           3          1           1
## 275           35           3          1           1
## 276           36           3          1           1
## 277           37           3          1           1
## 278           38           3          1           1
## 279           39           3          1           1
## 280           40           3          1           1
## 281           41           3          1           1
## 282           42           3          1           1
## 283           43           3          1           1
## 284           44           3          1           1
## 285           45           3          1           1
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## 289           49           3          1           1
## 290           50           3          1           1
## 291           51           3          1           1
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## 293           53           3          1           1
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## 297           57           3          1           1
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## 299           59           3          1           1
## 300           60           3          1           1
## 301           61           3          1           1
## 302           62           3          1           1
## 303           63           3          1           1
## 304           64           3          1           1
## 305           65           3          1           1
## 306           66           3          1           1
## 307           67           3          1           1
## 308           68           3          1           1
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## 310           70           3          1           1
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##  [ reached 'max' / getOption("max.print") -- omitted 12935001 rows ]
  • Each row is a meta-ecosystem.

  • It contains also “fake” meta-ecosystems which I created from unconnected ecosystems (metaecosystem type = Small-Large unconnected & metaecosystem type = Medium-Medium unconnected).

  • Warning appear after the following code, as:

  1. alpha diversity is computed for a culture that is totally crashed, so it has not meaning.
  2. beta diversity is computed between a culture that is still alive and one that is totally crashed. Because one of the cultures is totally crashed, the Bray-Curtis index is 1.
# --- COMPUTE META-ECOSYSTEMS FOR EACH TIME POINT --- #

ds_metaecosystems = NULL
row_i = 0
for (combination_i in 1:n_ecosystems_combinations) {
  for (time_point_selected in time_points) {
    
    row_i = row_i + 1
    
    current_day = sampling_days[time_point_selected + 1]
    current_system_nr = ecos_combin[combination_i, ]$system_nr
    current_combination = ecos_combin[combination_i, ]$ecosystems_combined
    current_disturbance = ecos_combin[combination_i, ]$disturbance
    current_metaeco_type = ecos_combin[combination_i, ]$metaecosystem_type
    current_connection = ecos_combin[combination_i, ]$connection
    current_IDs = c(ecos_combin[combination_i, ]$ID_first_ecosystem,
                    ecos_combin[combination_i, ]$ID_second_ecosystem)
    
    if (current_system_nr %in% metaecosystems_to_take_off)
      next
    
    if (current_IDs[1] == current_IDs[2])
      next
    
    species_vector_two_ecosystems = ds_ecosystems %>%
      filter(time_point == time_point_selected,
             culture_ID %in% current_IDs) %>%
      ungroup() %>%
      select(all_of(protist_species_indiv_per_ml))
    
    absence_presence_two_ecosystems <-
      ifelse(species_vector_two_ecosystems > 0, 1, 0)
    
    #Alpha diversity: Shannon (mean between the two ecosystems)
    
    shannon_ecosystem_1 = diversity(species_vector_two_ecosystems[1, ], index = "shannon")
    shannon_ecosystem_2 = diversity(species_vector_two_ecosystems[2, ], index = "shannon")
    shannon_value = (shannon_ecosystem_1 + shannon_ecosystem_2) / 2
    
    #Alpha diversity: Species richness (mean between the two ecosystems)
    
    richness_ecosystem_1 = specnumber(species_vector_two_ecosystems[1, ])
    richness_ecosystem_2 = specnumber(species_vector_two_ecosystems[2, ])
    mean_richness_value = (richness_ecosystem_1 + richness_ecosystem_2) / 2
    
    #Beta diversity: Jaccard
    
    jaccard_index_value = vegdist(species_vector_two_ecosystems,
                                  method = "jaccard") %>%
      as.numeric()
    
    #Beta diversity: Bray Curtis
    
    bray_curtis_value = vegdist(species_vector_two_ecosystems,
                                method = "bray") %>%
      as.numeric()
    
    #Beta diversity: partitioning of beta diversity from Sorensen index into turnover (Simpson pair-wise dissimilarity) and nestedness (nestedness-fraction of Sorensen)
    
    betapart_core_object = betapart.core(absence_presence_two_ecosystems)
    beta_spatial_turnover_value = beta.pair(betapart_core_object)$beta.sim %>% as.double()
    beta_nestedness_value = beta.pair(betapart_core_object)$beta.sne %>% as.double()
    beta_total_value = beta.pair(betapart_core_object)$beta.sor %>% as.double()
    
    #Gamma diversity: Meta-ecosystem richness
    
    metaecosystem_richness_value = colSums(species_vector_two_ecosystems) %>%
      specnumber()
    
    #Put everything together
    
    ds_metaecosystems[[row_i]] = ds_ecosystems %>%
      filter(culture_ID %in% current_IDs,
             time_point == time_point_selected) %>%
      summarise(total_metaecosystem_bioarea_mm2 = sum(bioarea_tot_mm2),
                total_metaecosystem_Ble_indiv = sum(Ble_tot_indiv),
                total_metaecosystem_Cep_indiv = sum(Cep_tot_indiv),
                total_metaecosystem_Col_indiv = sum(Col_tot_indiv),
                total_metaecosystem_Eug_indiv = sum(Eug_tot_indiv),
                total_metaecosystem_Eup_indiv = sum(Eup_tot_indiv),
                total_metaecosystem_Lox_indiv = sum(Lox_tot_indiv),
                total_metaecosystem_Pau_indiv = sum(Pau_tot_indiv),
                total_metaecosystem_Pca_indiv = sum(Pca_tot_indiv),
                total_metaecosystem_Spi_indiv = sum(Spi_tot_indiv),
                total_metaecosystem_Spi_te_indiv = sum(Spi_te_tot_indiv),
                total_metaecosystem_Tet_indiv = sum(Tet_tot_indiv),
                total_water_addition_ml = sum(water_addition_ml)) %>%
      mutate(system_nr = current_system_nr,
             ecosystems_combined = current_combination,
             metaecosystem_type = current_metaeco_type,
             ecosystem_size_symmetry = case_when(metaecosystem_type == "Small-Large" ~ "asymmetric",
                                                 metaecosystem_type == "Medium-Medium" ~ "symmetric",
                                                 metaecosystem_type == "Small-Small" ~ "symmetric",
                                                 metaecosystem_type == "Large-Large" ~ "symmetric"),
             connection = current_connection,
             disturbance = current_disturbance,
             time_point = time_point_selected,
             day = current_day,
             jaccard_index = jaccard_index_value,
             bray_curtis = bray_curtis_value,
             beta_spatial_turnover = beta_spatial_turnover_value,
             beta_nestedness = beta_nestedness_value,
             beta_total = beta_total_value,
             metaecosystem_richness = metaecosystem_richness_value,
             mean_shannon = shannon_value,
             mean_richness = mean_richness_value) %>%
      ungroup()
    
  }
}
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
##                  meaningless in method "jaccard"
## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
##                  meaningless in method "bray"
# Tidy up 

ds_metaecosystems = ds_metaecosystems %>%
  bind_rows() %>%
  as.data.frame() %>%
  select(time_point,
         day,
         system_nr,
         ecosystems_combined,
         disturbance,
         metaecosystem_type,
         ecosystem_size_symmetry,
         connection,
         mean_shannon,
         mean_richness,
         jaccard_index,
         bray_curtis,
         beta_spatial_turnover,
         beta_nestedness,
         beta_total,
         metaecosystem_richness,
         total_metaecosystem_bioarea_mm2,
         paste0("total_metaecosystem_", protist_species, "_indiv"),
         total_water_addition_ml)
# --- TEST CODE --- #

expect_equal(nrow(ds_metaecosystems), 
             n_time_points * n_ecosystems_combinations)

Meta-ecosystems

metaecosystem_type_selected = c("Medium-Medium", "Small-Large")

Alpha

response_variable_selected = "mean_shannon"


Plot original data - means
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- # 

# Create plots

p1=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Plot original data - single replicates
# --- ORIGINAL DATA - PLOT SINGLE REPLICATES --- # 

p1=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "high"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "low"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Prepare data for analysis
# --- PREPARE DATA --- #

# Add baselines

baselines = ds_metaecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(system_nr,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_metaecosystems %>%
  left_join(baselines)

# Filter and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         metaecosystem_type %in% metaecosystem_type_selected,
         #!is.na(total_water_addition_ml),
         !is.na(!!sym(response_variable_selected))) %>%
  mutate(metaecosystem_type = case_when(metaecosystem_type == "Small-Large unconnected" ~ "SL unc",
                                        metaecosystem_type == "Medium-Medium unconnected" ~ "MM unc",
                                        metaecosystem_type == "Small-Small meta-ecosystem" ~ "SS con",
                                        metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "MM con",
                                        metaecosystem_type == "Large-Large meta-ecosystem" ~ "LL con",
                                        metaecosystem_type == "Small-Large meta-ecosystem" ~ "SL con",
                                        TRUE ~ metaecosystem_type),
         type_conn = paste(metaecosystem_type, connection))
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI OF FILTERED DATA --- #

p1=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(1, 0.7))
Compute model results
# --- DEFINE MODEL FORMULA --- #

formula = paste("get(response_variable_selected) ~",
                "type_conn * disturbance * day +",
                "(day | baseline) +",
                "(day | system_nr)") %>%
  print()
## [1] "get(response_variable_selected) ~ type_conn * disturbance * day + (day | baseline) + (day | system_nr)"
# --- FIND ECOSYSTEM COMBINATIONS FOR ANALYSIS --- #

# Set up parameters

bootstrap_iterations = 1000

# Produce random (bootstrapped) rows

random_sets_of_sets <- runif(bootstrap_iterations, 
                             min = 1, 
                             max = nrow(ecos_combin_unconn_sets_of_sets)) %>% 
  round()

# Filter combinations according to the random rows

sets_of_sets_filtered = ecos_combin_unconn_sets_of_sets %>%
  filter(row_number() %in% random_sets_of_sets)
# --- DEFINE WHERE TO SAVE (AND FROM WHERE TO LATER READ) THE RESULTS OF THE ANALYSIS --- #

file_path = here("3_results", "tables", 
                      paste0("results_metaeco_", 
                             response_variable_selected, 
                             "_", 
                             bootstrap_iterations,
                             "_iterations",
                             ".csv"))
# --- FIND MODEL STATISTICS THROUGH MULTIPLE ITERATIONS RESHUFFLING ECOSYSTEM COMBINATIONS --- #

# Set parameters and initialise

results_table = list()
failed_optimizers = 0

# Fit models

for (comb_i in 1:bootstrap_iterations) {
  
  # Find system numbers
  
  system_nr_unconn_selected = ecos_combin_unconn_sets %>%
    filter(metaecosystem_type == "Small-Large" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_low |
           metaecosystem_type == "Small-Large" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_high |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_low |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_high) %>%
    pull(system_nr)
  
  # Prepare data for analysis
  
  data_for_analysis_comb_i = data_for_analysis %>%
    filter(system_nr %in% system_nr_unconn_selected | connection == "connected")
  
  # Run model
  
  model = try.different.optimizers.metaecos(data_for_analysis_comb_i,
                                            formula)
  
  # If all the optimisers fail, move on to the next iteration

  if (is.null(model)) {
    cat("This model could not be fitted with any optimiser (",
        system_nr_unconn_selected, 
        ") \n")
    
    failed_optimizers = failed_optimizers + 1
    
    next 
  }
  
  # Residuals - show Q-Q plot
  
  # print(qqnorm(resid(model))); print(qqline(resid(model)))
  
  # Residuals - save Residuals vs Fitted plot
  
  # plot = data_for_analysis_comb_i %>%
  #     mutate(predicted = fitted(model),
  #            residuals = resid(model)) %>%
  #     ggplot(aes(x = predicted,
  #                y = residuals)) +
  #     geom_point()
  # 
  # ggsave(here("3_results",
  #             "residual_plots",
  #               paste0("res_vs_fit_",
  #                      response_variable_selected,
  #                      "_combination_",
  #                      comb_i,
  #                      ".png")), 
  #          plot = plot, 
  #          width = 8, 
  #          height = 6)
  
  # Set up contrasts
  
  emmeans_output = emmeans(model,
                           specs = ~ type_conn * day * disturbance ,
                           method = "pairwise", 
                           adjust = "sidak",
                           bias.adj = TRUE,
                           lmer.df = "satterthwaite") 
  
  summary(emmeans_output)

  zeros = rep(0, 8)
  high_MM_conn = zeros; high_MM_conn[1] = 1
  high_MM_unc = zeros; high_MM_unc[2] = 1
  high_SL_conn = zeros; high_SL_conn[3] = 1
  high_SL_unc = zeros; high_SL_unc[4] = 1
  low_MM_conn = zeros; low_MM_conn[5] = 1
  low_MM_unc = zeros; low_MM_unc[6] = 1
  low_SL_conn = zeros; low_SL_conn[7] = 1
  low_SL_unc = zeros; low_SL_unc[8] = 1
  
  # Save contrasts in a table

  results_table[[comb_i]] = contrast(
    emmeans_output, 
    method = list("high SL_conn - SL_unc" = high_SL_conn - high_SL_unc,
                  "high MM_conn - MM_unc" = high_MM_conn - high_MM_unc,
                  "low SL_conn - SL_unc" = low_SL_conn - low_SL_unc,
                  "low MM_conn - MM_unc" = low_MM_conn - low_MM_unc)) %>%
    as.data.frame() %>%
    mutate(combination = comb_i,
           system_nr_unconnected_systems = paste(system_nr_unconn_selected, collapse = ", "))
  
}

# Tell how many optimizers failed

print(paste((failed_optimizers/bootstrap_iterations * 100), 
            "% of combinations created models that could not be fit"))

# Bind rows within the list results_table

results_table = results_table %>%
  bind_rows()

# Save the results

write.csv(results_table,
          file = file_path,
          row.names = F)
# --- READ THE RESULTS AFTER LENGTHY COMPUTATION --- #

results_table = read.csv(file = file_path)
Show iterated results - p value distributions
# --- SHOW ITERATED RESULTS - P VALUE DISTRIBUTIONS --- #

results_table %>% 
  filter(contrast == "high MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "high SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high SL_conn - SL_unc")

results_table %>% 
  filter(contrast == "low MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "low SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low SL_conn vs SL_unc")
Show iterated results - table with averaged values
# --- SHOW ITERATED RESULTS - TABLE WITH AVERAGED VALUES --- #

results_table %>%
  group_by(contrast) %>%
  summarise(estimate = median(estimate),
            SE = median(SE),
            df = median(df),
            t.ratio = median(t.ratio),
            p.value = median(p.value)) %>%
  as.data.frame() %>%
  mutate(estimate = round(estimate, digits = 3),
         SE = round(SE, digits = 3),
         df = round(df, digits = 3),
         t.ratio = round(t.ratio, digits = 3),
         p.value = round(p.value, digits = 3),
         evidence = "",
         evidence = ifelse(p.value > 0.1,
                           "none",
                           evidence),
         evidence = ifelse(p.value < 0.1,
                           "* weak",
                           evidence),
         evidence = ifelse(p.value < 0.05,
                           "** moderate",
                           evidence),
         evidence = ifelse(p.value < 0.01,
                           "*** strong",
                           evidence),
         evidence = ifelse(p.value < 0.001,
                           "**** very strong",
                           evidence),
         p.value = ifelse(p.value < 0.001,
                          "< 0.001",
                          p.value))
##                contrast estimate    SE    df t.ratio p.value   evidence
## 1 high MM_conn - MM_unc    0.115 0.078 37.56   1.497   0.142       none
## 2 high SL_conn - SL_unc    0.190 0.063 37.56   3.034   0.004 *** strong
## 3  low MM_conn - MM_unc   -0.003 0.078 37.56  -0.034   0.933       none
## 4  low SL_conn - SL_unc    0.182 0.059 37.56   3.075   0.004 *** strong

Beta

response_variable_selected = "bray_curtis"


Plot original data - means
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- # 

# Create plots

p1=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Plot original data - single replicates
# --- ORIGINAL DATA - PLOT SINGLE REPLICATES --- # 

p1=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "high"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "low"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Prepare data for analysis
# --- PREPARE DATA --- #

# Add baselines

baselines = ds_metaecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(system_nr,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_metaecosystems %>%
  left_join(baselines)

# Filter and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         metaecosystem_type %in% metaecosystem_type_selected,
         #!is.na(total_water_addition_ml),
         !is.na(!!sym(response_variable_selected))) %>%
  mutate(metaecosystem_type = case_when(metaecosystem_type == "Small-Large unconnected" ~ "SL unc",
                                        metaecosystem_type == "Medium-Medium unconnected" ~ "MM unc",
                                        metaecosystem_type == "Small-Small meta-ecosystem" ~ "SS con",
                                        metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "MM con",
                                        metaecosystem_type == "Large-Large meta-ecosystem" ~ "LL con",
                                        metaecosystem_type == "Small-Large meta-ecosystem" ~ "SL con",
                                        TRUE ~ metaecosystem_type),
         type_conn = paste(metaecosystem_type, connection))
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI OF FILTERED DATA --- #

p1=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(1, 0.7))
Compute model results
# --- DEFINE MODEL FORMULA --- #

formula = paste("get(response_variable_selected) ~",
                "type_conn * disturbance * day +",
                "(day | baseline) +",
                "(day | system_nr)") %>%
  print()
## [1] "get(response_variable_selected) ~ type_conn * disturbance * day + (day | baseline) + (day | system_nr)"
# --- FIND ECOSYSTEM COMBINATIONS FOR ANALYSIS --- #

# Set up parameters

bootstrap_iterations = 1000

# Produce random (bootstrapped) rows

random_sets_of_sets <- runif(bootstrap_iterations, 
                             min = 1, 
                             max = nrow(ecos_combin_unconn_sets_of_sets)) %>% 
  round()

# Filter combinations according to the random rows

sets_of_sets_filtered = ecos_combin_unconn_sets_of_sets %>%
  filter(row_number() %in% random_sets_of_sets)
# --- DEFINE WHERE TO SAVE (AND FROM WHERE TO LATER READ) THE RESULTS OF THE ANALYSIS --- #

file_path = here("3_results", "tables", 
                      paste0("results_metaeco_", 
                             response_variable_selected, 
                             "_", 
                             bootstrap_iterations,
                             "_iterations",
                             ".csv"))
# --- FIND MODEL STATISTICS THROUGH MULTIPLE ITERATIONS RESHUFFLING ECOSYSTEM COMBINATIONS --- #

# Set parameters and initialise

results_table = list()
failed_optimizers = 0

# Fit models

for (comb_i in 1:bootstrap_iterations) {
  
  # Find system numbers
  
  system_nr_unconn_selected = ecos_combin_unconn_sets %>%
    filter(metaecosystem_type == "Small-Large" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_low |
           metaecosystem_type == "Small-Large" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_high |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_low |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_high) %>%
    pull(system_nr)
  
  # Prepare data for analysis
  
  data_for_analysis_comb_i = data_for_analysis %>%
    filter(system_nr %in% system_nr_unconn_selected | connection == "connected")
  
  # Run model
  
  model = try.different.optimizers.metaecos(data_for_analysis_comb_i,
                                            formula)
  
  # If all the optimisers fail, move on to the next iteration

  if (is.null(model)) {
    cat("This model could not be fitted with any optimiser (",
        system_nr_unconn_selected, 
        ") \n")
    
    failed_optimizers = failed_optimizers + 1
    
    next 
  }
  
  # Residuals - show Q-Q plot
  
  # print(qqnorm(resid(model))); print(qqline(resid(model)))
  
  # Residuals - save Residuals vs Fitted plot
  
  # plot = data_for_analysis_comb_i %>%
  #     mutate(predicted = fitted(model),
  #            residuals = resid(model)) %>%
  #     ggplot(aes(x = predicted,
  #                y = residuals)) +
  #     geom_point()
  # 
  # ggsave(here("3_results",
  #             "residual_plots",
  #               paste0("res_vs_fit_",
  #                      response_variable_selected,
  #                      "_combination_",
  #                      comb_i,
  #                      ".png")), 
  #          plot = plot, 
  #          width = 8, 
  #          height = 6)
  
  # Set up contrasts
  
  emmeans_output = emmeans(model,
                           specs = ~ type_conn * day * disturbance ,
                           method = "pairwise", 
                           adjust = "sidak",
                           bias.adj = TRUE,
                           lmer.df = "satterthwaite") 
  
  summary(emmeans_output)

  zeros = rep(0, 8)
  high_MM_conn = zeros; high_MM_conn[1] = 1
  high_MM_unc = zeros; high_MM_unc[2] = 1
  high_SL_conn = zeros; high_SL_conn[3] = 1
  high_SL_unc = zeros; high_SL_unc[4] = 1
  low_MM_conn = zeros; low_MM_conn[5] = 1
  low_MM_unc = zeros; low_MM_unc[6] = 1
  low_SL_conn = zeros; low_SL_conn[7] = 1
  low_SL_unc = zeros; low_SL_unc[8] = 1
  
  # Save contrasts in a table

  results_table[[comb_i]] = contrast(
    emmeans_output, 
    method = list("high SL_conn - SL_unc" = high_SL_conn - high_SL_unc,
                  "high MM_conn - MM_unc" = high_MM_conn - high_MM_unc,
                  "low SL_conn - SL_unc" = low_SL_conn - low_SL_unc,
                  "low MM_conn - MM_unc" = low_MM_conn - low_MM_unc)) %>%
    as.data.frame() %>%
    mutate(combination = comb_i,
           system_nr_unconnected_systems = paste(system_nr_unconn_selected, collapse = ", "))
  
}

# Tell how many optimizers failed

print(paste((failed_optimizers/bootstrap_iterations * 100), 
            "% of combinations created models that could not be fit"))

# Bind rows within the list results_table

results_table = results_table %>%
  bind_rows()

# Save the results

write.csv(results_table,
          file = file_path,
          row.names = F)
# --- READ THE RESULTS AFTER LENGTHY COMPUTATION --- #

results_table = read.csv(file = file_path)
Show iterated results - p value distributions
# --- SHOW ITERATED RESULTS - P VALUE DISTRIBUTIONS --- #

results_table %>% 
  filter(contrast == "high MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "high SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high SL_conn - SL_unc")

results_table %>% 
  filter(contrast == "low MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "low SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low SL_conn vs SL_unc")
Show iterated results - table with averaged values
# --- SHOW ITERATED RESULTS - TABLE WITH AVERAGED VALUES --- #

results_table %>%
  group_by(contrast) %>%
  summarise(estimate = median(estimate),
            SE = median(SE),
            df = median(df),
            t.ratio = median(t.ratio),
            p.value = median(p.value)) %>%
  as.data.frame() %>%
  mutate(estimate = round(estimate, digits = 3),
         SE = round(SE, digits = 3),
         df = round(df, digits = 3),
         t.ratio = round(t.ratio, digits = 3),
         p.value = round(p.value, digits = 3),
         evidence = "",
         evidence = ifelse(p.value > 0.1,
                           "none",
                           evidence),
         evidence = ifelse(p.value < 0.1,
                           "* weak",
                           evidence),
         evidence = ifelse(p.value < 0.05,
                           "** moderate",
                           evidence),
         evidence = ifelse(p.value < 0.01,
                           "*** strong",
                           evidence),
         evidence = ifelse(p.value < 0.001,
                           "**** very strong",
                           evidence),
         p.value = ifelse(p.value < 0.001,
                          "< 0.001",
                          p.value))
##                contrast estimate    SE     df t.ratio p.value         evidence
## 1 high MM_conn - MM_unc    0.064 0.045 44.803   1.377   0.174             none
## 2 high SL_conn - SL_unc   -0.124 0.036 44.803  -3.407   0.001       *** strong
## 3  low MM_conn - MM_unc    0.065 0.045 44.803   1.432   0.157             none
## 4  low SL_conn - SL_unc   -0.129 0.034 44.803  -3.800 < 0.001 **** very strong

Gamma

response_variable_selected = "metaecosystem_richness"


Plot original data - means
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- # 

# Create plots

p1=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Plot original data - single replicates
# --- ORIGINAL DATA - PLOT SINGLE REPLICATES --- # 

p1=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "high"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "low"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Prepare data for analysis
# --- PREPARE DATA --- #

# Add baselines

baselines = ds_metaecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(system_nr,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_metaecosystems %>%
  left_join(baselines)

# Filter and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         metaecosystem_type %in% metaecosystem_type_selected,
         #!is.na(total_water_addition_ml),
         !is.na(!!sym(response_variable_selected))) %>%
  mutate(metaecosystem_type = case_when(metaecosystem_type == "Small-Large unconnected" ~ "SL unc",
                                        metaecosystem_type == "Medium-Medium unconnected" ~ "MM unc",
                                        metaecosystem_type == "Small-Small meta-ecosystem" ~ "SS con",
                                        metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "MM con",
                                        metaecosystem_type == "Large-Large meta-ecosystem" ~ "LL con",
                                        metaecosystem_type == "Small-Large meta-ecosystem" ~ "SL con",
                                        TRUE ~ metaecosystem_type),
         type_conn = paste(metaecosystem_type, connection))
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI OF FILTERED DATA --- #

p1=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(1, 0.7))
Compute model results
# --- DEFINE MODEL FORMULA --- #

formula = paste("get(response_variable_selected) ~",
                "type_conn * disturbance * day +",
                "(day | baseline) +",
                "(day | system_nr)") %>%
  print()
## [1] "get(response_variable_selected) ~ type_conn * disturbance * day + (day | baseline) + (day | system_nr)"
# --- FIND ECOSYSTEM COMBINATIONS FOR ANALYSIS --- #

# Set up parameters

bootstrap_iterations = 1000

# Produce random (bootstrapped) rows

random_sets_of_sets <- runif(bootstrap_iterations, 
                             min = 1, 
                             max = nrow(ecos_combin_unconn_sets_of_sets)) %>% 
  round()

# Filter combinations according to the random rows

sets_of_sets_filtered = ecos_combin_unconn_sets_of_sets %>%
  filter(row_number() %in% random_sets_of_sets)
# --- DEFINE WHERE TO SAVE (AND FROM WHERE TO LATER READ) THE RESULTS OF THE ANALYSIS --- #

file_path = here("3_results", "tables", 
                      paste0("results_metaeco_", 
                             response_variable_selected, 
                             "_", 
                             bootstrap_iterations,
                             "_iterations",
                             ".csv"))
# --- FIND MODEL STATISTICS THROUGH MULTIPLE ITERATIONS RESHUFFLING ECOSYSTEM COMBINATIONS --- #

# Set parameters and initialise

results_table = list()
failed_optimizers = 0

# Fit models

for (comb_i in 1:bootstrap_iterations) {
  
  # Find system numbers
  
  system_nr_unconn_selected = ecos_combin_unconn_sets %>%
    filter(metaecosystem_type == "Small-Large" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_low |
           metaecosystem_type == "Small-Large" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_high |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_low |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_high) %>%
    pull(system_nr)
  
  # Prepare data for analysis
  
  data_for_analysis_comb_i = data_for_analysis %>%
    filter(system_nr %in% system_nr_unconn_selected | connection == "connected")
  
  # Run model
  
  model = try.different.optimizers.metaecos(data_for_analysis_comb_i,
                                            formula)
  
  # If all the optimisers fail, move on to the next iteration

  if (is.null(model)) {
    cat("This model could not be fitted with any optimiser (",
        system_nr_unconn_selected, 
        ") \n")
    
    failed_optimizers = failed_optimizers + 1
    
    next 
  }
  
  # Residuals - show Q-Q plot
  
  # print(qqnorm(resid(model))); print(qqline(resid(model)))
  
  # Residuals - save Residuals vs Fitted plot
  
  # plot = data_for_analysis_comb_i %>%
  #     mutate(predicted = fitted(model),
  #            residuals = resid(model)) %>%
  #     ggplot(aes(x = predicted,
  #                y = residuals)) +
  #     geom_point()
  # 
  # ggsave(here("3_results",
  #             "residual_plots",
  #               paste0("res_vs_fit_",
  #                      response_variable_selected,
  #                      "_combination_",
  #                      comb_i,
  #                      ".png")), 
  #          plot = plot, 
  #          width = 8, 
  #          height = 6)
  
  # Set up contrasts
  
  emmeans_output = emmeans(model,
                           specs = ~ type_conn * day * disturbance ,
                           method = "pairwise", 
                           adjust = "sidak",
                           bias.adj = TRUE,
                           lmer.df = "satterthwaite") 
  
  summary(emmeans_output)

  zeros = rep(0, 8)
  high_MM_conn = zeros; high_MM_conn[1] = 1
  high_MM_unc = zeros; high_MM_unc[2] = 1
  high_SL_conn = zeros; high_SL_conn[3] = 1
  high_SL_unc = zeros; high_SL_unc[4] = 1
  low_MM_conn = zeros; low_MM_conn[5] = 1
  low_MM_unc = zeros; low_MM_unc[6] = 1
  low_SL_conn = zeros; low_SL_conn[7] = 1
  low_SL_unc = zeros; low_SL_unc[8] = 1
  
  # Save contrasts in a table

  results_table[[comb_i]] = contrast(
    emmeans_output, 
    method = list("high SL_conn - SL_unc" = high_SL_conn - high_SL_unc,
                  "high MM_conn - MM_unc" = high_MM_conn - high_MM_unc,
                  "low SL_conn - SL_unc" = low_SL_conn - low_SL_unc,
                  "low MM_conn - MM_unc" = low_MM_conn - low_MM_unc)) %>%
    as.data.frame() %>%
    mutate(combination = comb_i,
           system_nr_unconnected_systems = paste(system_nr_unconn_selected, collapse = ", "))
  
}

# Tell how many optimizers failed

print(paste((failed_optimizers/bootstrap_iterations * 100), 
            "% of combinations created models that could not be fit"))

# Bind rows within the list results_table

results_table = results_table %>%
  bind_rows()

# Save the results

write.csv(results_table,
          file = file_path,
          row.names = F)
# --- READ THE RESULTS AFTER LENGTHY COMPUTATION --- #

results_table = read.csv(file = file_path)
Show iterated results - p value distributions
# --- SHOW ITERATED RESULTS - P VALUE DISTRIBUTIONS --- #

results_table %>% 
  filter(contrast == "high MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "high SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high SL_conn - SL_unc")

results_table %>% 
  filter(contrast == "low MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "low SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low SL_conn vs SL_unc")
Show iterated results - table with averaged values
# --- SHOW ITERATED RESULTS - TABLE WITH AVERAGED VALUES --- #

results_table %>%
  group_by(contrast) %>%
  summarise(estimate = median(estimate),
            SE = median(SE),
            df = median(df),
            t.ratio = median(t.ratio),
            p.value = median(p.value)) %>%
  as.data.frame() %>%
  mutate(estimate = round(estimate, digits = 3),
         SE = round(SE, digits = 3),
         df = round(df, digits = 3),
         t.ratio = round(t.ratio, digits = 3),
         p.value = round(p.value, digits = 3),
         evidence = "",
         evidence = ifelse(p.value > 0.1,
                           "none",
                           evidence),
         evidence = ifelse(p.value < 0.1,
                           "* weak",
                           evidence),
         evidence = ifelse(p.value < 0.05,
                           "** moderate",
                           evidence),
         evidence = ifelse(p.value < 0.01,
                           "*** strong",
                           evidence),
         evidence = ifelse(p.value < 0.001,
                           "**** very strong",
                           evidence),
         p.value = ifelse(p.value < 0.001,
                          "< 0.001",
                          p.value))
##                contrast estimate    SE     df t.ratio p.value    evidence
## 1 high MM_conn - MM_unc    0.367 0.442 39.171   0.822   0.416        none
## 2 high SL_conn - SL_unc   -0.339 0.353 38.411  -0.950   0.348        none
## 3  low MM_conn - MM_unc    0.967 0.445 39.581   2.173   0.036 ** moderate
## 4  low SL_conn - SL_unc    0.033 0.333 38.467   0.097   0.872        none

Biomass

response_variable_selected = "total_metaecosystem_bioarea_mm2"


Plot original data - means
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- # 

# Create plots

p1=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(ds_metaecosystems %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Plot original data - single replicates
# --- ORIGINAL DATA - PLOT SINGLE REPLICATES --- # 

p1=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "high"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.replicates(ds_metaecosystems %>% filter(disturbance == "low"),
                            metaecosystem_type_selected,
                            response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(0.9, 1),
          common.legend = TRUE,
          align = "v")
Prepare data for analysis
# --- PREPARE DATA --- #

# Add baselines

baselines = ds_metaecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(system_nr,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_metaecosystems %>%
  left_join(baselines)

# Filter and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         metaecosystem_type %in% metaecosystem_type_selected,
         #!is.na(total_water_addition_ml),
         !is.na(!!sym(response_variable_selected))) %>%
  mutate(metaecosystem_type = case_when(metaecosystem_type == "Small-Large unconnected" ~ "SL unc",
                                        metaecosystem_type == "Medium-Medium unconnected" ~ "MM unc",
                                        metaecosystem_type == "Small-Small meta-ecosystem" ~ "SS con",
                                        metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "MM con",
                                        metaecosystem_type == "Large-Large meta-ecosystem" ~ "LL con",
                                        metaecosystem_type == "Small-Large meta-ecosystem" ~ "SL con",
                                        TRUE ~ metaecosystem_type),
         type_conn = paste(metaecosystem_type, connection))
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI OF FILTERED DATA --- #

p1=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "high"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2=plot.metaecos.points(data_for_analysis %>% filter(disturbance == "low"),
                        metaecosystem_type_selected,
                        response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2,
          heights = c(1, 0.7))
Compute model results
# --- DEFINE MODEL FORMULA --- #

formula = paste("get(response_variable_selected) ~",
                "type_conn * disturbance * day +",
                "(day | baseline) +",
                "(day | system_nr)") %>%
  print()
## [1] "get(response_variable_selected) ~ type_conn * disturbance * day + (day | baseline) + (day | system_nr)"
# --- FIND ECOSYSTEM COMBINATIONS FOR ANALYSIS --- #

# Set up parameters

bootstrap_iterations = 1000

# Produce random (bootstrapped) rows

random_sets_of_sets <- runif(bootstrap_iterations, 
                             min = 1, 
                             max = nrow(ecos_combin_unconn_sets_of_sets)) %>% 
  round()

# Filter combinations according to the random rows

sets_of_sets_filtered = ecos_combin_unconn_sets_of_sets %>%
  filter(row_number() %in% random_sets_of_sets)
# --- DEFINE WHERE TO SAVE (AND FROM WHERE TO LATER READ) THE RESULTS OF THE ANALYSIS --- #

file_path = here("3_results", "tables", 
                      paste0("results_metaeco_", 
                             response_variable_selected, 
                             "_", 
                             bootstrap_iterations,
                             "_iterations",
                             ".csv"))
# --- FIND MODEL STATISTICS THROUGH MULTIPLE ITERATIONS RESHUFFLING ECOSYSTEM COMBINATIONS --- #

# Set parameters and initialise

results_table = list()
failed_optimizers = 0

# Fit models

for (comb_i in 1:bootstrap_iterations) {
  
  # Find system numbers
  
  system_nr_unconn_selected = ecos_combin_unconn_sets %>%
    filter(metaecosystem_type == "Small-Large" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_low |
           metaecosystem_type == "Small-Large" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_SL_high |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "low" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_low |
           metaecosystem_type == "Medium-Medium" & 
           disturbance == "high" & 
           set == sets_of_sets_filtered[comb_i, ]$set_MM_high) %>%
    pull(system_nr)
  
  # Prepare data for analysis
  
  data_for_analysis_comb_i = data_for_analysis %>%
    filter(system_nr %in% system_nr_unconn_selected | connection == "connected")
  
  # Run model
  
  model = try.different.optimizers.metaecos(data_for_analysis_comb_i,
                                            formula)
  
  # If all the optimisers fail, move on to the next iteration

  if (is.null(model)) {
    cat("This model could not be fitted with any optimiser (",
        system_nr_unconn_selected, 
        ") \n")
    
    failed_optimizers = failed_optimizers + 1
    
    next 
  }
  
  # Residuals - show Q-Q plot
  
  # print(qqnorm(resid(model))); print(qqline(resid(model)))
  
  # Residuals - save Residuals vs Fitted plot
  
  # plot = data_for_analysis_comb_i %>%
  #     mutate(predicted = fitted(model),
  #            residuals = resid(model)) %>%
  #     ggplot(aes(x = predicted,
  #                y = residuals)) +
  #     geom_point()
  # 
  # ggsave(here("3_results",
  #             "residual_plots",
  #               paste0("res_vs_fit_",
  #                      response_variable_selected,
  #                      "_combination_",
  #                      comb_i,
  #                      ".png")), 
  #          plot = plot, 
  #          width = 8, 
  #          height = 6)
  
  # Set up contrasts
  
  emmeans_output = emmeans(model,
                           specs = ~ type_conn * day * disturbance ,
                           method = "pairwise", 
                           adjust = "sidak",
                           bias.adj = TRUE,
                           lmer.df = "satterthwaite") 
  
  summary(emmeans_output)

  zeros = rep(0, 8)
  high_MM_conn = zeros; high_MM_conn[1] = 1
  high_MM_unc = zeros; high_MM_unc[2] = 1
  high_SL_conn = zeros; high_SL_conn[3] = 1
  high_SL_unc = zeros; high_SL_unc[4] = 1
  low_MM_conn = zeros; low_MM_conn[5] = 1
  low_MM_unc = zeros; low_MM_unc[6] = 1
  low_SL_conn = zeros; low_SL_conn[7] = 1
  low_SL_unc = zeros; low_SL_unc[8] = 1
  
  # Save contrasts in a table

  results_table[[comb_i]] = contrast(
    emmeans_output, 
    method = list("high SL_conn - SL_unc" = high_SL_conn - high_SL_unc,
                  "high MM_conn - MM_unc" = high_MM_conn - high_MM_unc,
                  "low SL_conn - SL_unc" = low_SL_conn - low_SL_unc,
                  "low MM_conn - MM_unc" = low_MM_conn - low_MM_unc)) %>%
    as.data.frame() %>%
    mutate(combination = comb_i,
           system_nr_unconnected_systems = paste(system_nr_unconn_selected, collapse = ", "))
  
}

# Tell how many optimizers failed

print(paste((failed_optimizers/bootstrap_iterations * 100), 
            "% of combinations created models that could not be fit"))

# Bind rows within the list results_table

results_table = results_table %>%
  bind_rows()

# Save the results

write.csv(results_table,
          file = file_path,
          row.names = F)
# --- READ THE RESULTS AFTER LENGTHY COMPUTATION --- #

results_table = read.csv(file = file_path)
Show iterated results - p value distributions
# --- SHOW ITERATED RESULTS - P VALUE DISTRIBUTIONS --- #

results_table %>% 
  filter(contrast == "high MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "high SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values high SL_conn - SL_unc")

results_table %>% 
  filter(contrast == "low MM_conn - MM_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low MM_conn - MM_unc")

results_table %>% 
  filter(contrast == "low SL_conn - SL_unc") %>% 
  pull(p.value) %>% 
  hist(main = "p values low SL_conn vs SL_unc")
Show iterated results - table with averaged values
# --- SHOW ITERATED RESULTS - TABLE WITH AVERAGED VALUES --- #

results_table %>%
  group_by(contrast) %>%
  summarise(estimate = median(estimate),
            SE = median(SE),
            df = median(df),
            t.ratio = median(t.ratio),
            p.value = median(p.value)) %>%
  as.data.frame() %>%
  mutate(estimate = round(estimate, digits = 3),
         SE = round(SE, digits = 3),
         df = round(df, digits = 3),
         t.ratio = round(t.ratio, digits = 3),
         p.value = round(p.value, digits = 3),
         evidence = "",
         evidence = ifelse(p.value > 0.1,
                           "none",
                           evidence),
         evidence = ifelse(p.value < 0.1,
                           "* weak",
                           evidence),
         evidence = ifelse(p.value < 0.05,
                           "** moderate",
                           evidence),
         evidence = ifelse(p.value < 0.01,
                           "*** strong",
                           evidence),
         evidence = ifelse(p.value < 0.001,
                           "**** very strong",
                           evidence),
         p.value = ifelse(p.value < 0.001,
                          "< 0.001",
                          p.value))
##                contrast estimate     SE     df t.ratio p.value    evidence
## 1 high MM_conn - MM_unc   17.326 13.109 33.314   1.325   0.194        none
## 2 high SL_conn - SL_unc  -32.905 10.510 33.314  -3.106   0.004  *** strong
## 3  low MM_conn - MM_unc   38.759 13.109 33.314   2.945   0.006  *** strong
## 4  low SL_conn - SL_unc  -21.448  9.909 33.314  -2.164   0.038 ** moderate

Ecosystems

Shannon

response_variable_selected = "shannon"
Plot original data
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Prepare data for analysis
# --- PREPARE DATA FOR ANALYSIS --- #

# Add baselines

baselines = ds_ecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(culture_ID,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_ecosystems %>%
  left_join(baselines)

# Filter data and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         #!is.na(water_addition_ml),
         !is.na(!!sym(response_variable_selected)),
         !is.infinite(!!sym(response_variable_selected))) %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L",
                                    ecosystem_type == "Small connected to small" ~ "S_S",
                                    ecosystem_type == "Small connected to large" ~ "S_L",
                                    ecosystem_type == "Medium connected to medium" ~ "M_M",
                                    ecosystem_type == "Large connected to large" ~ "L_L",
                                    ecosystem_type == "Large connected to small" ~ "L_S",
                                    TRUE ~ ecosystem_type)) %>%
  ungroup()
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Compute model results
# --- MODEL - CONSTRUCT --- #

# Define formula

formula = paste("get(response_variable_selected) ~",
                "ecosystem_type * disturbance * day +",
                "(day | culture_ID) +",
                "(day | baseline)") %>%
  print()
## [1] "get(response_variable_selected) ~ ecosystem_type * disturbance * day + (day | culture_ID) + (day | baseline)"
# Construct model

model = try.different.optimizers.ecos(data_for_analysis,
                                      formula)
## [1] "Model successfully fitted with optimizer: bobyqa "
# --- MODEL - SUMMARY --- #

print(summary(model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: formula
##    Data: data
## Control: lmerControl(optimizer = opt$optimizer)
## 
##      AIC      BIC   logLik deviance df.resid 
##    352.4    526.4   -137.2    274.4      602 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.5   -0.6    0.0    0.7    3.7 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 0e+00    0e+00         
##             day         1e-18    1e-09     NaN 
##  baseline   (Intercept) 4e-11    7e-06         
##             day         2e-13    5e-07    -1.00
##  Residual               9e-02    3e-01         
## Number of obs: 641, groups:  culture_ID, 109; baseline, 109
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             1e+00      2e-01  6e+02     9.6
## ecosystem_typeL_L                      -6e-02      2e-01  6e+02    -0.3
## ecosystem_typeL_S                      -3e-01      2e-01  6e+02    -1.2
## ecosystem_typeM                        -3e-01      2e-01  6e+02    -1.3
## ecosystem_typeM_M                      -6e-02      2e-01  6e+02    -0.3
## ecosystem_typeS                         1e-01      2e-01  6e+02     0.6
## ecosystem_typeS_L                       5e-01      2e-01  6e+02     2.5
## ecosystem_typeS_S                       3e-01      2e-01  6e+02     1.7
## disturbancelow                          4e-01      2e-01  6e+02     1.6
## day                                    -7e-04      8e-03  6e+02    -0.1
## ecosystem_typeL_L:disturbancelow       -3e-01      3e-01  6e+02    -1.0
## ecosystem_typeL_S:disturbancelow       -3e-01      3e-01  6e+02    -0.9
## ecosystem_typeM:disturbancelow         -4e-01      3e-01  6e+02    -1.2
## ecosystem_typeM_M:disturbancelow       -4e-01      3e-01  6e+02    -1.5
## ecosystem_typeS:disturbancelow         -2e-01      3e-01  6e+02    -0.6
## ecosystem_typeS_L:disturbancelow       -1e+00      3e-01  6e+02    -3.2
## ecosystem_typeS_S:disturbancelow       -4e-01      3e-01  6e+02    -1.6
## ecosystem_typeL_L:day                   2e-03      1e-02  6e+02     0.2
## ecosystem_typeL_S:day                   8e-03      1e-02  6e+02     0.7
## ecosystem_typeM:day                     3e-03      1e-02  6e+02     0.3
## ecosystem_typeM_M:day                  -2e-03      1e-02  6e+02    -0.2
## ecosystem_typeS:day                    -7e-02      1e-02  6e+02    -5.1
## ecosystem_typeS_L:day                  -6e-02      1e-02  6e+02    -5.7
## ecosystem_typeS_S:day                  -7e-02      1e-02  6e+02    -6.5
## disturbancelow:day                     -2e-02      1e-02  6e+02    -1.4
## ecosystem_typeL_L:disturbancelow:day    1e-02      1e-02  6e+02     0.8
## ecosystem_typeL_S:disturbancelow:day    2e-02      2e-02  6e+02     1.0
## ecosystem_typeM:disturbancelow:day      2e-02      2e-02  6e+02     1.4
## ecosystem_typeM_M:disturbancelow:day    2e-02      1e-02  6e+02     1.3
## ecosystem_typeS:disturbancelow:day      4e-02      2e-02  6e+02     2.3
## ecosystem_typeS_L:disturbancelow:day    8e-02      2e-02  6e+02     5.0
## ecosystem_typeS_S:disturbancelow:day    4e-02      1e-02  6e+02     2.8
##                                      Pr(>|t|)    
## (Intercept)                            <2e-16 ***
## ecosystem_typeL_L                       0.732    
## ecosystem_typeL_S                       0.240    
## ecosystem_typeM                         0.205    
## ecosystem_typeM_M                       0.741    
## ecosystem_typeS                         0.579    
## ecosystem_typeS_L                       0.014 *  
## ecosystem_typeS_S                       0.086 .  
## disturbancelow                          0.109    
## day                                     0.930    
## ecosystem_typeL_L:disturbancelow        0.318    
## ecosystem_typeL_S:disturbancelow        0.361    
## ecosystem_typeM:disturbancelow          0.228    
## ecosystem_typeM_M:disturbancelow        0.128    
## ecosystem_typeS:disturbancelow          0.555    
## ecosystem_typeS_L:disturbancelow        0.002 ** 
## ecosystem_typeS_S:disturbancelow        0.119    
## ecosystem_typeL_L:day                   0.810    
## ecosystem_typeL_S:day                   0.485    
## ecosystem_typeM:day                     0.781    
## ecosystem_typeM_M:day                   0.836    
## ecosystem_typeS:day                     4e-07 ***
## ecosystem_typeS_L:day                   2e-08 ***
## ecosystem_typeS_S:day                   2e-10 ***
## disturbancelow:day                      0.149    
## ecosystem_typeL_L:disturbancelow:day    0.429    
## ecosystem_typeL_S:disturbancelow:day    0.295    
## ecosystem_typeM:disturbancelow:day      0.155    
## ecosystem_typeM_M:disturbancelow:day    0.196    
## ecosystem_typeS:disturbancelow:day      0.022 *  
## ecosystem_typeS_L:disturbancelow:day    6e-07 ***
## ecosystem_typeS_S:disturbancelow:day    0.005 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# --- MODEL - ANOVA --- #

car::Anova(model, type = "III")
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: get(response_variable_selected)
##                                   Chisq Df Pr(>Chisq)    
## (Intercept)                     92.1969  1  < 2.2e-16 ***
## ecosystem_type                  26.7429  7  0.0003707 ***
## disturbance                      2.5795  1  0.1082569    
## day                              0.0077  1  0.9302887    
## ecosystem_type:disturbance      11.9786  7  0.1012636    
## ecosystem_type:day             155.7995  7  < 2.2e-16 ***
## disturbance:day                  2.0906  1  0.1482065    
## ecosystem_type:disturbance:day  37.7566  7  3.371e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# --- ESTIMATE MARGINAL MEANS --- #

emmeans_output = emmeans(model,
                         specs = ~ ecosystem_type * disturbance * day,
                         adjust = "sidak",
                         bias.adj = TRUE,
                         lmer.df = "satterthwaite") 

emmeans_output
##  ecosystem_type disturbance  day emmean     SE  df lower.CL upper.CL
##  L              high        17.8  1.468 0.0547 641    1.306    1.630
##  L_L            high        17.8  1.446 0.0387 641    1.331    1.560
##  L_S            high        17.8  1.353 0.0547 641    1.191    1.515
##  M              high        17.8  1.248 0.0547 641    1.086    1.410
##  M_M            high        17.8  1.370 0.0387 641    1.255    1.484
##  S              high        17.8  0.336 0.0736 641    0.118    0.554
##  S_L            high        17.8  0.854 0.0547 641    0.692    1.016
##  S_S            high        17.8  0.621 0.0412 641    0.499    0.743
##  L              low         17.8  1.526 0.0547 641    1.364    1.688
##  L_L            low         17.8  1.433 0.0387 641    1.318    1.547
##  L_S            low         17.8  1.429 0.0547 641    1.267    1.591
##  M              low         17.8  1.341 0.0547 641    1.179    1.503
##  M_M            low         17.8  1.341 0.0387 641    1.226    1.455
##  S              low         17.8  0.939 0.0557 641    0.774    1.104
##  S_L            low         17.8  1.373 0.0547 641    1.211    1.535
##  S_S            low         17.8  0.966 0.0387 641    0.852    1.081
## 
## Degrees-of-freedom method: satterthwaite 
## Results are given on the get (not the response) scale. 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 16 estimates
# --- CODE EACH LEVEL OF DISTURBANCE AND ECOSYSTEM TYPE TO THEN PRODUCE CONTRASTS --- #

high_L = c(1, rep(0,15)) 
high_L_L = c(rep(0,1), 1, rep(0,14)) 
high_L_S = c(rep(0,2), 1, rep(0,13)) 
high_M = c(rep(0,3), 1, rep(0,12)) 
high_M_M = c(rep(0,4), 1, rep(0,11)) 
high_S = c(rep(0,5), 1, rep(0,10)) 
high_S_L = c(rep(0,6), 1, rep(0,9)) 
high_S_S = c(rep(0,7), 1, rep(0,8)) 
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
# --- PRODUCE ECOSYSTEM TYPE CONTRASTS --- #

# Set parameters

n_of_digits = 3

# Compute constrasts

contrasts = contrast(emmeans_output, 
                     method = list("high S_L - S" = high_S_L - high_S,
                                   "high S_L - S_S" = high_S_L - high_S_S,
                                   "high S_S - S" = high_S_S - high_S,
                                   "high M_M - M" = high_M_M - high_M,
                                   "high L_S - L" = high_L_S - high_L,
                                   "high L_S - L_L" = high_L_S - high_L_L,
                                   "high L_L - L" = high_L_L - high_L,
                                   "low S_L - S" = low_S_L - low_S,
                                   "low S_L - S_S" = low_S_L - low_S_S,
                                   "low S_S - S" = low_S_S - low_S,
                                   "low M_M - M" = low_M_M - low_M,
                                   "low L_S - L" = low_L_S - low_L,
                                   "low L_S - L_L" = low_L_S - low_L_L,
                                   "low L_L - L" = low_L_L - low_L)) %>%
  as.data.frame() %>%
  mutate(p.value = round(p.value, digits = n_of_digits),
         estimate = round(estimate, digits = n_of_digits),
         SE = round(SE, digits = n_of_digits),
         df = round(df, digits = n_of_digits),
         t.ratio = round(t.ratio, digits = n_of_digits),
         e = "",
         e = ifelse(p.value > 0.1, 
                           "",
                           e),
         e = ifelse(p.value < 0.05, 
                           "*",
                           e),
         e = ifelse(p.value < 0.01, 
                           "**",
                           e),
         e = ifelse(p.value < 0.001, 
                           "***",
                           e)) %>%
  rename(" " = e)
Show results
# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #

contrasts
##          contrast estimate    SE  df t.ratio p.value    
## 1    high S_L - S    0.518 0.092 641   5.647   0.000 ***
## 2  high S_L - S_S    0.233 0.068 641   3.399   0.001  **
## 3    high S_S - S    0.285 0.084 641   3.382   0.001  **
## 4    high M_M - M    0.122 0.067 641   1.817   0.070    
## 5    high L_S - L   -0.115 0.077 641  -1.490   0.137    
## 6  high L_S - L_L   -0.093 0.067 641  -1.384   0.167    
## 7    high L_L - L   -0.023 0.067 641  -0.337   0.736    
## 8     low S_L - S    0.434 0.078 641   5.562   0.000 ***
## 9   low S_L - S_S    0.407 0.067 641   6.071   0.000 ***
## 10    low S_S - S    0.027 0.068 641   0.402   0.688    
## 11    low M_M - M   -0.001 0.067 641  -0.009   0.993    
## 12    low L_S - L   -0.098 0.077 641  -1.261   0.208    
## 13  low L_S - L_L   -0.004 0.067 641  -0.060   0.952    
## 14    low L_L - L   -0.094 0.067 641  -1.395   0.163


Show model residuals residuals
# --- PLOT MODEL RESIDUALS --- #

# Simulate residuals from the fitted model

simulationOutput <- simulateResiduals(fittedModel = model, 
                                      n = 1000) 

# Test for overdispersion in the model to check if variance exceeds mean

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0037, p-value = 0.948
## alternative hypothesis: two.sided
# Plot Q-Q and Residuals vs Fitted plots

plot(simulationOutput)

Biomass

response_variable_selected = "bioarea_mm2_per_ml"
Plot original data
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Prepare data for analysis
# --- PREPARE DATA FOR ANALYSIS --- #

# Add baselines

baselines = ds_ecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(culture_ID,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_ecosystems %>%
  left_join(baselines)

# Filter data and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         #!is.na(water_addition_ml),
         !is.na(!!sym(response_variable_selected)),
         !is.infinite(!!sym(response_variable_selected))) %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L",
                                    ecosystem_type == "Small connected to small" ~ "S_S",
                                    ecosystem_type == "Small connected to large" ~ "S_L",
                                    ecosystem_type == "Medium connected to medium" ~ "M_M",
                                    ecosystem_type == "Large connected to large" ~ "L_L",
                                    ecosystem_type == "Large connected to small" ~ "L_S",
                                    TRUE ~ ecosystem_type)) %>%
  ungroup()
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Compute model results
# --- MODEL - CONSTRUCT --- #

# Define formula

formula = paste("get(response_variable_selected) ~",
                "ecosystem_type * disturbance * day +",
                "(day | culture_ID) +",
                "(day | baseline)") %>%
  print()
## [1] "get(response_variable_selected) ~ ecosystem_type * disturbance * day + (day | culture_ID) + (day | baseline)"
# Construct model

model = try.different.optimizers.ecos(data_for_analysis,
                                      formula)
## [1] "Model successfully fitted with optimizer: bobyqa "
# --- MODEL - SUMMARY --- #

print(summary(model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: formula
##    Data: data
## Control: lmerControl(optimizer = opt$optimizer)
## 
##      AIC      BIC   logLik deviance df.resid 
##   1639.4   1814.3   -780.7   1561.4      615 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.1   -0.6    0.0    0.5    3.6 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 2e-01    0.39          
##             day         2e-04    0.01     -1.00
##  baseline   (Intercept) 1e-01    0.34          
##             day         2e-04    0.01     -1.00
##  Residual               6e-01    0.77          
## Number of obs: 654, groups:  culture_ID, 109; baseline, 109
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                              5.94       0.46 122.57    12.9
## ecosystem_typeL_L                       -0.15       0.56 122.57    -0.3
## ecosystem_typeL_S                       -1.18       0.65 122.57    -1.8
## ecosystem_typeM                         -1.63       0.65 122.57    -2.5
## ecosystem_typeM_M                       -0.26       0.56 122.57    -0.5
## ecosystem_typeS                         -4.14       0.69 122.57    -6.0
## ecosystem_typeS_L                       -2.90       0.65 122.57    -4.5
## ecosystem_typeS_S                       -3.72       0.56 122.57    -6.6
## disturbancelow                          -0.99       0.65 122.57    -1.5
## day                                     -0.16       0.02 167.67    -7.2
## ecosystem_typeL_L:disturbancelow         0.68       0.80 122.57     0.9
## ecosystem_typeL_S:disturbancelow         1.68       0.92 122.57     1.8
## ecosystem_typeM:disturbancelow           1.80       0.92 122.57     2.0
## ecosystem_typeM_M:disturbancelow         1.35       0.80 122.57     1.7
## ecosystem_typeS:disturbancelow           3.12       0.95 122.57     3.3
## ecosystem_typeS_L:disturbancelow         1.90       0.92 122.57     2.1
## ecosystem_typeS_S:disturbancelow         2.37       0.80 122.57     3.0
## ecosystem_typeL_L:day                   -0.01       0.03 167.67    -0.3
## ecosystem_typeL_S:day                    0.01       0.03 167.67     0.4
## ecosystem_typeM:day                      0.02       0.03 167.67     0.7
## ecosystem_typeM_M:day                   -0.03       0.03 167.67    -1.1
## ecosystem_typeS:day                      0.09       0.03 167.67     2.5
## ecosystem_typeS_L:day                    0.04       0.03 167.67     1.3
## ecosystem_typeS_S:day                    0.07       0.03 167.67     2.7
## disturbancelow:day                       0.07       0.03 167.67     2.2
## ecosystem_typeL_L:disturbancelow:day    -0.05       0.04 167.67    -1.3
## ecosystem_typeL_S:disturbancelow:day    -0.08       0.04 167.67    -1.7
## ecosystem_typeM:disturbancelow:day      -0.10       0.04 167.67    -2.3
## ecosystem_typeM_M:disturbancelow:day    -0.05       0.04 167.67    -1.4
## ecosystem_typeS:disturbancelow:day      -0.15       0.05 167.67    -3.2
## ecosystem_typeS_L:disturbancelow:day    -0.08       0.04 167.67    -1.8
## ecosystem_typeS_S:disturbancelow:day    -0.12       0.04 167.67    -3.1
##                                      Pr(>|t|)    
## (Intercept)                            <2e-16 ***
## ecosystem_typeL_L                       0.789    
## ecosystem_typeL_S                       0.073 .  
## ecosystem_typeM                         0.013 *  
## ecosystem_typeM_M                       0.643    
## ecosystem_typeS                         2e-08 ***
## ecosystem_typeS_L                       2e-05 ***
## ecosystem_typeS_S                       1e-09 ***
## disturbancelow                          0.130    
## day                                     2e-11 ***
## ecosystem_typeL_L:disturbancelow        0.395    
## ecosystem_typeL_S:disturbancelow        0.070 .  
## ecosystem_typeM:disturbancelow          0.052 .  
## ecosystem_typeM_M:disturbancelow        0.093 .  
## ecosystem_typeS:disturbancelow          0.001 ** 
## ecosystem_typeS_L:disturbancelow        0.041 *  
## ecosystem_typeS_S:disturbancelow        0.004 ** 
## ecosystem_typeL_L:day                   0.728    
## ecosystem_typeL_S:day                   0.695    
## ecosystem_typeM:day                     0.474    
## ecosystem_typeM_M:day                   0.258    
## ecosystem_typeS:day                     0.012 *  
## ecosystem_typeS_L:day                   0.203    
## ecosystem_typeS_S:day                   0.009 ** 
## disturbancelow:day                      0.026 *  
## ecosystem_typeL_L:disturbancelow:day    0.213    
## ecosystem_typeL_S:disturbancelow:day    0.086 .  
## ecosystem_typeM:disturbancelow:day      0.021 *  
## ecosystem_typeM_M:disturbancelow:day    0.163    
## ecosystem_typeS:disturbancelow:day      0.002 ** 
## ecosystem_typeS_L:disturbancelow:day    0.081 .  
## ecosystem_typeS_S:disturbancelow:day    0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# --- MODEL - ANOVA --- #

car::Anova(model, type = "III")
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: get(response_variable_selected)
##                                   Chisq Df Pr(>Chisq)    
## (Intercept)                    166.6820  1  < 2.2e-16 ***
## ecosystem_type                 124.6134  7  < 2.2e-16 ***
## disturbance                      2.3252  1    0.12729    
## day                             51.2279  1  8.224e-13 ***
## ecosystem_type:disturbance      18.2609  7    0.01085 *  
## ecosystem_type:day              33.5306  7  2.108e-05 ***
## disturbance:day                  5.0218  1    0.02503 *  
## ecosystem_type:disturbance:day  17.2032  7    0.01613 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# --- ESTIMATE MARGINAL MEANS --- #

emmeans_output = emmeans(model,
                         specs = ~ ecosystem_type * disturbance * day,
                         adjust = "sidak",
                         bias.adj = TRUE,
                         lmer.df = "satterthwaite") 

emmeans_output
##  ecosystem_type disturbance day emmean    SE  df lower.CL upper.CL
##  L              high         18  3.061 0.161 127    2.576    3.547
##  L_L            high         18  2.739 0.114 127    2.396    3.082
##  L_S            high         18  2.108 0.161 127    1.623    2.593
##  M              high         18  1.838 0.161 127    1.352    2.323
##  M_M            high         18  2.241 0.114 127    1.898    2.584
##  S              high         18  0.448 0.181 127   -0.094    0.991
##  S_L            high         18  0.891 0.161 127    0.406    1.376
##  S_S            high         18  0.647 0.114 127    0.304    0.990
##  L              low          18  3.343 0.161 127    2.858    3.828
##  L_L            low          18  2.831 0.114 127    2.488    3.174
##  L_S            low          18  2.682 0.161 127    2.196    3.167
##  M              low          18  2.057 0.161 127    1.572    2.543
##  M_M            low          18  2.898 0.114 127    2.555    3.242
##  S              low          18  1.214 0.161 127    0.728    1.699
##  S_L            low          18  1.662 0.161 127    1.176    2.147
##  S_S            low          18  1.154 0.114 127    0.811    1.497
## 
## Degrees-of-freedom method: satterthwaite 
## Results are given on the get (not the response) scale. 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 16 estimates
# --- CODE EACH LEVEL OF DISTURBANCE AND ECOSYSTEM TYPE TO THEN PRODUCE CONTRASTS --- #

high_L = c(1, rep(0,15)) 
high_L_L = c(rep(0,1), 1, rep(0,14)) 
high_L_S = c(rep(0,2), 1, rep(0,13)) 
high_M = c(rep(0,3), 1, rep(0,12)) 
high_M_M = c(rep(0,4), 1, rep(0,11)) 
high_S = c(rep(0,5), 1, rep(0,10)) 
high_S_L = c(rep(0,6), 1, rep(0,9)) 
high_S_S = c(rep(0,7), 1, rep(0,8)) 
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
# --- PRODUCE ECOSYSTEM TYPE CONTRASTS --- #

# Set parameters

n_of_digits = 3

# Compute constrasts

contrasts = contrast(emmeans_output, 
                     method = list("high S_L - S" = high_S_L - high_S,
                                   "high S_L - S_S" = high_S_L - high_S_S,
                                   "high S_S - S" = high_S_S - high_S,
                                   "high M_M - M" = high_M_M - high_M,
                                   "high L_S - L" = high_L_S - high_L,
                                   "high L_S - L_L" = high_L_S - high_L_L,
                                   "high L_L - L" = high_L_L - high_L,
                                   "low S_L - S" = low_S_L - low_S,
                                   "low S_L - S_S" = low_S_L - low_S_S,
                                   "low S_S - S" = low_S_S - low_S,
                                   "low M_M - M" = low_M_M - low_M,
                                   "low L_S - L" = low_L_S - low_L,
                                   "low L_S - L_L" = low_L_S - low_L_L,
                                   "low L_L - L" = low_L_L - low_L)) %>%
  as.data.frame() %>%
  mutate(p.value = round(p.value, digits = n_of_digits),
         estimate = round(estimate, digits = n_of_digits),
         SE = round(SE, digits = n_of_digits),
         df = round(df, digits = n_of_digits),
         t.ratio = round(t.ratio, digits = n_of_digits),
         e = "",
         e = ifelse(p.value > 0.1, 
                           "",
                           e),
         e = ifelse(p.value < 0.05, 
                           "*",
                           e),
         e = ifelse(p.value < 0.01, 
                           "**",
                           e),
         e = ifelse(p.value < 0.001, 
                           "***",
                           e)) %>%
  rename(" " = e)
Show results
# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #

contrasts
##          contrast estimate    SE      df t.ratio p.value    
## 1    high S_L - S    0.442 0.242 126.838   1.826   0.070    
## 2  high S_L - S_S    0.244 0.198 126.838   1.233   0.220    
## 3    high S_S - S    0.199 0.214 126.838   0.930   0.354    
## 4    high M_M - M    0.404 0.198 126.838   2.041   0.043   *
## 5    high L_S - L   -0.953 0.228 126.838  -4.175   0.000 ***
## 6  high L_S - L_L   -0.631 0.198 126.838  -3.190   0.002  **
## 7    high L_L - L   -0.322 0.198 126.838  -1.631   0.105    
## 8     low S_L - S    0.448 0.228 126.838   1.962   0.052    
## 9   low S_L - S_S    0.507 0.198 126.838   2.565   0.011   *
## 10    low S_S - S   -0.059 0.198 126.838  -0.300   0.765    
## 11    low M_M - M    0.841 0.198 126.838   4.253   0.000 ***
## 12    low L_S - L   -0.662 0.228 126.838  -2.897   0.004  **
## 13  low L_S - L_L   -0.149 0.198 126.838  -0.755   0.452    
## 14    low L_L - L   -0.512 0.198 126.838  -2.591   0.011   *


Show model residuals residuals
# --- PLOT MODEL RESIDUALS --- #

# Simulate residuals from the fitted model

simulationOutput <- simulateResiduals(fittedModel = model, 
                                      n = 1000) 

# Test for overdispersion in the model to check if variance exceeds mean

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0057, p-value = 0.894
## alternative hypothesis: two.sided
# Plot Q-Q and Residuals vs Fitted plots

plot(simulationOutput)

Richness

response_variable_selected = "species_richness"
Plot original data
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Prepare data for analysis
# --- PREPARE DATA FOR ANALYSIS --- #

# Add baselines

baselines = ds_ecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(culture_ID,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_ecosystems %>%
  left_join(baselines)

# Filter data and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         #!is.na(water_addition_ml),
         !is.na(!!sym(response_variable_selected)),
         !is.infinite(!!sym(response_variable_selected))) %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L",
                                    ecosystem_type == "Small connected to small" ~ "S_S",
                                    ecosystem_type == "Small connected to large" ~ "S_L",
                                    ecosystem_type == "Medium connected to medium" ~ "M_M",
                                    ecosystem_type == "Large connected to large" ~ "L_L",
                                    ecosystem_type == "Large connected to small" ~ "L_S",
                                    TRUE ~ ecosystem_type)) %>%
  ungroup()
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text

p2 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Compute model results
# --- MODEL - CONSTRUCT --- #

# Define formula

formula = paste("get(response_variable_selected) ~",
                "ecosystem_type * disturbance * day +",
                "(day | culture_ID) +",
                "(day | baseline)") %>%
  print()
## [1] "get(response_variable_selected) ~ ecosystem_type * disturbance * day + (day | culture_ID) + (day | baseline)"
# Construct model

model = try.different.optimizers.ecos(data_for_analysis,
                                      formula)
## [1] "Model successfully fitted with optimizer: bobyqa "
# --- MODEL - SUMMARY --- #

print(summary(model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: formula
##    Data: data
## Control: lmerControl(optimizer = opt$optimizer)
## 
##      AIC      BIC   logLik deviance df.resid 
##   2273.8   2448.7  -1097.9   2195.8      615 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.6   -0.6    0.0    0.6    3.2 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 7e-05    0.008         
##             day         9e-06    0.003    -1.00
##  baseline   (Intercept) 1e-01    0.321         
##             day         7e-05    0.009    -1.00
##  Residual               2e+00    1.289         
## Number of obs: 654, groups:  culture_ID, 109; baseline, 8
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             7e+00      7e-01  3e+02    10.5
## ecosystem_typeL_L                       3e-01      8e-01  5e+02     0.4
## ecosystem_typeL_S                      -8e-01      9e-01  5e+02    -0.9
## ecosystem_typeM                         3e-01      9e-01  5e+02     0.4
## ecosystem_typeM_M                       5e-01      8e-01  5e+02     0.6
## ecosystem_typeS                        -1e+00      1e+00  5e+02    -1.2
## ecosystem_typeS_L                       1e+00      9e-01  5e+02     1.0
## ecosystem_typeS_S                      -9e-01      8e-01  5e+02    -1.1
## disturbancelow                          5e-01      9e-01  5e+02     0.6
## day                                    -2e-02      3e-02  5e+02    -0.5
## ecosystem_typeL_L:disturbancelow       -8e-01      1e+00  5e+02    -0.7
## ecosystem_typeL_S:disturbancelow       -5e-01      1e+00  5e+02    -0.4
## ecosystem_typeM:disturbancelow         -6e-01      1e+00  5e+02    -0.5
## ecosystem_typeM_M:disturbancelow       -5e-01      1e+00  5e+02    -0.5
## ecosystem_typeS:disturbancelow          2e+00      1e+00  5e+02     1.5
## ecosystem_typeS_L:disturbancelow       -1e+00      1e+00  5e+02    -1.1
## ecosystem_typeS_S:disturbancelow        1e+00      1e+00  5e+02     0.8
## ecosystem_typeL_L:day                  -4e-02      4e-02  6e+02    -1.0
## ecosystem_typeL_S:day                  -4e-03      5e-02  6e+02    -0.1
## ecosystem_typeM:day                    -9e-02      5e-02  6e+02    -1.8
## ecosystem_typeM_M:day                  -8e-02      4e-02  6e+02    -1.9
## ecosystem_typeS:day                    -2e-01      5e-02  6e+02    -4.1
## ecosystem_typeS_L:day                  -2e-01      5e-02  6e+02    -5.1
## ecosystem_typeS_S:day                  -2e-01      4e-02  6e+02    -4.5
## disturbancelow:day                     -7e-03      5e-02  6e+02    -0.1
## ecosystem_typeL_L:disturbancelow:day    2e-02      6e-02  6e+02     0.3
## ecosystem_typeL_S:disturbancelow:day    3e-02      7e-02  6e+02     0.5
## ecosystem_typeM:disturbancelow:day      3e-02      7e-02  6e+02     0.4
## ecosystem_typeM_M:disturbancelow:day    4e-02      6e-02  6e+02     0.6
## ecosystem_typeS:disturbancelow:day     -2e-02      7e-02  6e+02    -0.3
## ecosystem_typeS_L:disturbancelow:day    2e-01      7e-02  6e+02     2.5
## ecosystem_typeS_S:disturbancelow:day    7e-04      6e-02  6e+02     0.0
##                                      Pr(>|t|)    
## (Intercept)                            <2e-16 ***
## ecosystem_typeL_L                        0.69    
## ecosystem_typeL_S                        0.37    
## ecosystem_typeM                          0.72    
## ecosystem_typeM_M                        0.53    
## ecosystem_typeS                          0.23    
## ecosystem_typeS_L                        0.31    
## ecosystem_typeS_S                        0.27    
## disturbancelow                           0.57    
## day                                      0.59    
## ecosystem_typeL_L:disturbancelow         0.49    
## ecosystem_typeL_S:disturbancelow         0.69    
## ecosystem_typeM:disturbancelow           0.64    
## ecosystem_typeM_M:disturbancelow         0.65    
## ecosystem_typeS:disturbancelow           0.15    
## ecosystem_typeS_L:disturbancelow         0.27    
## ecosystem_typeS_S:disturbancelow         0.40    
## ecosystem_typeL_L:day                    0.31    
## ecosystem_typeL_S:day                    0.93    
## ecosystem_typeM:day                      0.07 .  
## ecosystem_typeM_M:day                    0.06 .  
## ecosystem_typeS:day                     4e-05 ***
## ecosystem_typeS_L:day                   5e-07 ***
## ecosystem_typeS_S:day                   7e-06 ***
## disturbancelow:day                       0.89    
## ecosystem_typeL_L:disturbancelow:day     0.73    
## ecosystem_typeL_S:disturbancelow:day     0.65    
## ecosystem_typeM:disturbancelow:day       0.72    
## ecosystem_typeM_M:disturbancelow:day     0.52    
## ecosystem_typeS:disturbancelow:day       0.80    
## ecosystem_typeS_L:disturbancelow:day     0.01 *  
## ecosystem_typeS_S:disturbancelow:day     0.99    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# --- MODEL - ANOVA --- #

car::Anova(model, type = "III")
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: get(response_variable_selected)
##                                   Chisq Df Pr(>Chisq)    
## (Intercept)                    110.2649  1  < 2.2e-16 ***
## ecosystem_type                  11.8520  7     0.1055    
## disturbance                      0.3227  1     0.5700    
## day                              0.2915  1     0.5893    
## ecosystem_type:disturbance      11.0533  7     0.1363    
## ecosystem_type:day              63.3876  7  3.169e-11 ***
## disturbance:day                  0.0199  1     0.8879    
## ecosystem_type:disturbance:day  10.9139  7     0.1424    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# --- ESTIMATE MARGINAL MEANS --- #

emmeans_output = emmeans(model,
                         specs = ~ ecosystem_type * disturbance * day,
                         adjust = "sidak",
                         bias.adj = TRUE,
                         lmer.df = "satterthwaite") 

emmeans_output
##  ecosystem_type disturbance day emmean    SE    df lower.CL upper.CL
##  L              high         18   6.84 0.251 115.7    6.081     7.59
##  L_L            high         18   6.40 0.181  77.8    5.845     6.95
##  L_S            high         18   5.92 0.250 116.9    5.168     6.67
##  M              high         18   5.58 0.248 124.6    4.835     6.32
##  M_M            high         18   5.94 0.183  69.6    5.381     6.50
##  S              high         18   1.78 0.277 128.8    0.948     2.61
##  S_L            high         18   3.34 0.248 125.2    2.596     4.09
##  S_S            high         18   2.46 0.182  75.3    1.902     3.01
##  L              low          18   7.25 0.252 114.4    6.492     8.01
##  L_L            low          18   6.38 0.182  74.8    5.826     6.94
##  L_S            low          18   6.38 0.250 115.3    5.621     7.13
##  M              low          18   5.81 0.255 108.3    5.042     6.58
##  M_M            low          18   6.51 0.183  69.1    5.947     7.06
##  S              low          18   3.87 0.250 117.8    3.119     4.62
##  S_L            low          18   5.42 0.249 120.2    4.674     6.17
##  S_S            low          18   3.86 0.187  64.8    3.292     4.44
## 
## Degrees-of-freedom method: satterthwaite 
## Results are given on the get (not the response) scale. 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 16 estimates
# --- CODE EACH LEVEL OF DISTURBANCE AND ECOSYSTEM TYPE TO THEN PRODUCE CONTRASTS --- #

high_L = c(1, rep(0,15)) 
high_L_L = c(rep(0,1), 1, rep(0,14)) 
high_L_S = c(rep(0,2), 1, rep(0,13)) 
high_M = c(rep(0,3), 1, rep(0,12)) 
high_M_M = c(rep(0,4), 1, rep(0,11)) 
high_S = c(rep(0,5), 1, rep(0,10)) 
high_S_L = c(rep(0,6), 1, rep(0,9)) 
high_S_S = c(rep(0,7), 1, rep(0,8)) 
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
# --- PRODUCE ECOSYSTEM TYPE CONTRASTS --- #

# Set parameters

n_of_digits = 3

# Compute constrasts

contrasts = contrast(emmeans_output, 
                     method = list("high S_L - S" = high_S_L - high_S,
                                   "high S_L - S_S" = high_S_L - high_S_S,
                                   "high S_S - S" = high_S_S - high_S,
                                   "high M_M - M" = high_M_M - high_M,
                                   "high L_S - L" = high_L_S - high_L,
                                   "high L_S - L_L" = high_L_S - high_L_L,
                                   "high L_L - L" = high_L_L - high_L,
                                   "low S_L - S" = low_S_L - low_S,
                                   "low S_L - S_S" = low_S_L - low_S_S,
                                   "low S_S - S" = low_S_S - low_S,
                                   "low M_M - M" = low_M_M - low_M,
                                   "low L_S - L" = low_L_S - low_L,
                                   "low L_S - L_L" = low_L_S - low_L_L,
                                   "low L_L - L" = low_L_L - low_L)) %>%
  as.data.frame() %>%
  mutate(p.value = round(p.value, digits = n_of_digits),
         estimate = round(estimate, digits = n_of_digits),
         SE = round(SE, digits = n_of_digits),
         df = round(df, digits = n_of_digits),
         t.ratio = round(t.ratio, digits = n_of_digits),
         e = "",
         e = ifelse(p.value > 0.1, 
                           "",
                           e),
         e = ifelse(p.value < 0.05, 
                           "*",
                           e),
         e = ifelse(p.value < 0.01, 
                           "**",
                           e),
         e = ifelse(p.value < 0.001, 
                           "***",
                           e)) %>%
  rename(" " = e)
Show results
# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #

contrasts
##          contrast estimate    SE      df t.ratio p.value    
## 1    high S_L - S    1.560 0.363 155.966   4.300   0.000 ***
## 2  high S_L - S_S    0.886 0.293 154.170   3.021   0.003  **
## 3    high S_S - S    0.674 0.316 153.687   2.133   0.035   *
## 4    high M_M - M    0.359 0.293 154.093   1.225   0.222    
## 5    high L_S - L   -0.916 0.336 151.815  -2.723   0.007  **
## 6  high L_S - L_L   -0.474 0.294 154.833  -1.614   0.109    
## 7    high L_L - L   -0.442 0.295 155.519  -1.498   0.136    
## 8     low S_L - S    1.550 0.338 153.410   4.587   0.000 ***
## 9   low S_L - S_S    1.557 0.291 151.585   5.348   0.000 ***
## 10    low S_S - S   -0.007 0.293 153.952  -0.024   0.981    
## 11    low M_M - M    0.694 0.295 155.458   2.350   0.020   *
## 12    low L_S - L   -0.874 0.343 156.316  -2.551   0.012   *
## 13  low L_S - L_L   -0.006 0.294 155.074  -0.021   0.983    
## 14    low L_L - L   -0.868 0.294 155.060  -2.949   0.004  **


Show model residuals residuals
# --- PLOT MODEL RESIDUALS --- #

# Simulate residuals from the fitted model

simulationOutput <- simulateResiduals(fittedModel = model, 
                                      n = 1000) 

# Test for overdispersion in the model to check if variance exceeds mean

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.004, p-value = 0.96
## alternative hypothesis: two.sided
# Plot Q-Q and Residuals vs Fitted plots

plot(simulationOutput)

Evenness

response_variable_selected = "evenness_pielou"
Plot original data
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Prepare data for analysis
# --- PREPARE DATA FOR ANALYSIS --- #

# Add baselines

baselines = ds_ecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(culture_ID,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_ecosystems %>%
  left_join(baselines)

# Filter data and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         #!is.na(water_addition_ml),
         !is.na(!!sym(response_variable_selected)),
         !is.infinite(!!sym(response_variable_selected))) %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L",
                                    ecosystem_type == "Small connected to small" ~ "S_S",
                                    ecosystem_type == "Small connected to large" ~ "S_L",
                                    ecosystem_type == "Medium connected to medium" ~ "M_M",
                                    ecosystem_type == "Large connected to large" ~ "L_L",
                                    ecosystem_type == "Large connected to small" ~ "L_S",
                                    TRUE ~ ecosystem_type)) %>%
  ungroup()
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Compute model results
# --- MODEL - CONSTRUCT --- #

# Define formula

formula = paste("get(response_variable_selected) ~",
                "ecosystem_type * disturbance * day +",
                "(day | culture_ID) +",
                "(day | baseline)") %>%
  print()
## [1] "get(response_variable_selected) ~ ecosystem_type * disturbance * day + (day | culture_ID) + (day | baseline)"
# Construct model

model = try.different.optimizers.ecos(data_for_analysis,
                                      formula)
## [1] "Model successfully fitted with optimizer: bobyqa "
# --- MODEL - SUMMARY --- #

print(summary(model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: formula
##    Data: data
## Control: lmerControl(optimizer = opt$optimizer)
## 
##      AIC      BIC   logLik deviance df.resid 
##   -692.0   -519.8    385.0   -770.0      573 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -5.7   -0.5    0.1    0.6    3.9 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 6e-16    2e-08         
##             day         1e-18    1e-09    -1.00
##  baseline   (Intercept) 4e-12    2e-06         
##             day         2e-14    1e-07    -1.00
##  Residual               2e-02    1e-01         
## Number of obs: 612, groups:  culture_ID, 109; baseline, 109
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             8e-01      7e-02  6e+02    11.4
## ecosystem_typeL_L                      -6e-02      8e-02  6e+02    -0.8
## ecosystem_typeL_S                      -8e-02      9e-02  6e+02    -0.9
## ecosystem_typeM                        -2e-01      9e-02  6e+02    -2.2
## ecosystem_typeM_M                      -8e-02      8e-02  6e+02    -0.9
## ecosystem_typeS                         5e-01      1e-01  6e+02     4.3
## ecosystem_typeS_L                       6e-02      1e-01  6e+02     0.6
## ecosystem_typeS_S                       5e-01      8e-02  6e+02     5.5
## disturbancelow                          2e-01      9e-02  6e+02     1.6
## day                                     5e-04      3e-03  6e+02     0.2
## ecosystem_typeL_L:disturbancelow       -9e-02      1e-01  6e+02    -0.8
## ecosystem_typeL_S:disturbancelow       -1e-01      1e-01  6e+02    -0.9
## ecosystem_typeM:disturbancelow         -8e-02      1e-01  6e+02    -0.6
## ecosystem_typeM_M:disturbancelow       -2e-01      1e-01  6e+02    -1.5
## ecosystem_typeS:disturbancelow         -5e-01      1e-01  6e+02    -3.5
## ecosystem_typeS_L:disturbancelow       -3e-01      1e-01  6e+02    -2.2
## ecosystem_typeS_S:disturbancelow       -6e-01      1e-01  6e+02    -5.3
## ecosystem_typeL_L:day                   5e-03      4e-03  6e+02     1.1
## ecosystem_typeL_S:day                   5e-03      5e-03  6e+02     1.0
## ecosystem_typeM:day                     1e-02      5e-03  6e+02     2.3
## ecosystem_typeM_M:day                   5e-03      4e-03  6e+02     1.1
## ecosystem_typeS:day                    -5e-02      6e-03  6e+02    -8.0
## ecosystem_typeS_L:day                   4e-03      5e-03  6e+02     0.7
## ecosystem_typeS_S:day                  -3e-02      4e-03  6e+02    -6.8
## disturbancelow:day                     -8e-03      5e-03  6e+02    -1.6
## ecosystem_typeL_L:disturbancelow:day    4e-03      6e-03  6e+02     0.7
## ecosystem_typeL_S:disturbancelow:day    6e-03      7e-03  6e+02     0.9
## ecosystem_typeM:disturbancelow:day      6e-03      7e-03  6e+02     0.9
## ecosystem_typeM_M:disturbancelow:day    6e-03      6e-03  6e+02     1.0
## ecosystem_typeS:disturbancelow:day      5e-02      8e-03  6e+02     6.3
## ecosystem_typeS_L:disturbancelow:day    1e-02      7e-03  6e+02     1.6
## ecosystem_typeS_S:disturbancelow:day    4e-02      6e-03  6e+02     6.7
##                                      Pr(>|t|)    
## (Intercept)                            <2e-16 ***
## ecosystem_typeL_L                        0.44    
## ecosystem_typeL_S                        0.37    
## ecosystem_typeM                          0.03 *  
## ecosystem_typeM_M                        0.35    
## ecosystem_typeS                         2e-05 ***
## ecosystem_typeS_L                        0.52    
## ecosystem_typeS_S                       7e-08 ***
## disturbancelow                           0.10    
## day                                      0.88    
## ecosystem_typeL_L:disturbancelow         0.42    
## ecosystem_typeL_S:disturbancelow         0.38    
## ecosystem_typeM:disturbancelow           0.53    
## ecosystem_typeM_M:disturbancelow         0.13    
## ecosystem_typeS:disturbancelow          6e-04 ***
## ecosystem_typeS_L:disturbancelow         0.03 *  
## ecosystem_typeS_S:disturbancelow        1e-07 ***
## ecosystem_typeL_L:day                    0.26    
## ecosystem_typeL_S:day                    0.30    
## ecosystem_typeM:day                      0.02 *  
## ecosystem_typeM_M:day                    0.25    
## ecosystem_typeS:day                     7e-15 ***
## ecosystem_typeS_L:day                    0.47    
## ecosystem_typeS_S:day                   3e-11 ***
## disturbancelow:day                       0.11    
## ecosystem_typeL_L:disturbancelow:day     0.50    
## ecosystem_typeL_S:disturbancelow:day     0.37    
## ecosystem_typeM:disturbancelow:day       0.37    
## ecosystem_typeM_M:disturbancelow:day     0.30    
## ecosystem_typeS:disturbancelow:day      6e-10 ***
## ecosystem_typeS_L:disturbancelow:day     0.10    
## ecosystem_typeS_S:disturbancelow:day    6e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# --- MODEL - ANOVA --- #

car::Anova(model, type = "III")
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: get(response_variable_selected)
##                                   Chisq Df Pr(>Chisq)    
## (Intercept)                    130.1357  1  < 2.2e-16 ***
## ecosystem_type                 121.9831  7  < 2.2e-16 ***
## disturbance                      2.6800  1     0.1016    
## day                              0.0240  1     0.8769    
## ecosystem_type:disturbance      53.2690  7   3.28e-09 ***
## ecosystem_type:day             225.4252  7  < 2.2e-16 ***
## disturbance:day                  2.5267  1     0.1119    
## ecosystem_type:disturbance:day 111.4767  7  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# --- ESTIMATE MARGINAL MEANS --- #

emmeans_output = emmeans(model,
                         specs = ~ ecosystem_type * disturbance * day,
                         adjust = "sidak",
                         bias.adj = TRUE,
                         lmer.df = "satterthwaite") 

emmeans_output
##  ecosystem_type disturbance  day emmean     SE  df lower.CL upper.CL
##  L              high        17.7  0.767 0.0236 612    0.697    0.836
##  L_L            high        17.7  0.789 0.0167 612    0.739    0.838
##  L_S            high        17.7  0.772 0.0236 612    0.702    0.842
##  M              high        17.7  0.756 0.0236 612    0.687    0.826
##  M_M            high        17.7  0.777 0.0167 612    0.728    0.826
##  S              high        17.7  0.415 0.0349 612    0.312    0.518
##  S_L            high        17.7  0.899 0.0276 612    0.817    0.981
##  S_S            high        17.7  0.687 0.0199 612    0.629    0.746
##  L              low         17.7  0.783 0.0236 612    0.713    0.853
##  L_L            low         17.7  0.783 0.0167 612    0.734    0.832
##  L_S            low         17.7  0.782 0.0236 612    0.712    0.852
##  M              low         17.7  0.799 0.0236 612    0.730    0.869
##  M_M            low         17.7  0.729 0.0167 612    0.680    0.779
##  S              low         17.7  0.783 0.0249 612    0.709    0.856
##  S_L            low         17.7  0.823 0.0236 612    0.753    0.893
##  S_S            low         17.7  0.814 0.0176 612    0.762    0.866
## 
## Degrees-of-freedom method: satterthwaite 
## Results are given on the get (not the response) scale. 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 16 estimates
# --- CODE EACH LEVEL OF DISTURBANCE AND ECOSYSTEM TYPE TO THEN PRODUCE CONTRASTS --- #

high_L = c(1, rep(0,15)) 
high_L_L = c(rep(0,1), 1, rep(0,14)) 
high_L_S = c(rep(0,2), 1, rep(0,13)) 
high_M = c(rep(0,3), 1, rep(0,12)) 
high_M_M = c(rep(0,4), 1, rep(0,11)) 
high_S = c(rep(0,5), 1, rep(0,10)) 
high_S_L = c(rep(0,6), 1, rep(0,9)) 
high_S_S = c(rep(0,7), 1, rep(0,8)) 
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
# --- PRODUCE ECOSYSTEM TYPE CONTRASTS --- #

# Set parameters

n_of_digits = 3

# Compute constrasts

contrasts = contrast(emmeans_output, 
                     method = list("high S_L - S" = high_S_L - high_S,
                                   "high S_L - S_S" = high_S_L - high_S_S,
                                   "high S_S - S" = high_S_S - high_S,
                                   "high M_M - M" = high_M_M - high_M,
                                   "high L_S - L" = high_L_S - high_L,
                                   "high L_S - L_L" = high_L_S - high_L_L,
                                   "high L_L - L" = high_L_L - high_L,
                                   "low S_L - S" = low_S_L - low_S,
                                   "low S_L - S_S" = low_S_L - low_S_S,
                                   "low S_S - S" = low_S_S - low_S,
                                   "low M_M - M" = low_M_M - low_M,
                                   "low L_S - L" = low_L_S - low_L,
                                   "low L_S - L_L" = low_L_S - low_L_L,
                                   "low L_L - L" = low_L_L - low_L)) %>%
  as.data.frame() %>%
  mutate(p.value = round(p.value, digits = n_of_digits),
         estimate = round(estimate, digits = n_of_digits),
         SE = round(SE, digits = n_of_digits),
         df = round(df, digits = n_of_digits),
         t.ratio = round(t.ratio, digits = n_of_digits),
         e = "",
         e = ifelse(p.value > 0.1, 
                           "",
                           e),
         e = ifelse(p.value < 0.05, 
                           "*",
                           e),
         e = ifelse(p.value < 0.01, 
                           "**",
                           e),
         e = ifelse(p.value < 0.001, 
                           "***",
                           e)) %>%
  rename(" " = e)
Show results
# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #

contrasts
##          contrast estimate    SE  df t.ratio p.value    
## 1    high S_L - S    0.484 0.044 612  10.869   0.000 ***
## 2  high S_L - S_S    0.211 0.034 612   6.207   0.000 ***
## 3    high S_S - S    0.272 0.040 612   6.786   0.000 ***
## 4    high M_M - M    0.021 0.029 612   0.715   0.475    
## 5    high L_S - L    0.006 0.033 612   0.166   0.868    
## 6  high L_S - L_L   -0.017 0.029 612  -0.575   0.566    
## 7    high L_L - L    0.022 0.029 612   0.766   0.444    
## 8     low S_L - S    0.040 0.034 612   1.173   0.241    
## 9   low S_L - S_S    0.009 0.029 612   0.299   0.765    
## 10    low S_S - S    0.031 0.030 612   1.032   0.303    
## 11    low M_M - M   -0.070 0.029 612  -2.423   0.016   *
## 12    low L_S - L   -0.001 0.033 612  -0.027   0.978    
## 13  low L_S - L_L   -0.001 0.029 612  -0.023   0.982    
## 14    low L_L - L    0.000 0.029 612  -0.009   0.993


Show model residuals residuals
# --- PLOT MODEL RESIDUALS --- #

# Simulate residuals from the fitted model

simulationOutput <- simulateResiduals(fittedModel = model, 
                                      n = 1000) 

# Test for overdispersion in the model to check if variance exceeds mean

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0036, p-value = 0.944
## alternative hypothesis: two.sided
# Plot Q-Q and Residuals vs Fitted plots

plot(simulationOutput)

Median Size

response_variable_selected = "median_body_area_µm2"
Plot original data
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Prepare data for analysis
# --- PREPARE DATA FOR ANALYSIS --- #

# Add baselines

baselines = ds_ecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(culture_ID,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_ecosystems %>%
  left_join(baselines)

# Filter data and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         #!is.na(water_addition_ml),
         !is.na(!!sym(response_variable_selected)),
         !is.infinite(!!sym(response_variable_selected))) %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L",
                                    ecosystem_type == "Small connected to small" ~ "S_S",
                                    ecosystem_type == "Small connected to large" ~ "S_L",
                                    ecosystem_type == "Medium connected to medium" ~ "M_M",
                                    ecosystem_type == "Large connected to large" ~ "L_L",
                                    ecosystem_type == "Large connected to small" ~ "L_S",
                                    TRUE ~ ecosystem_type)) %>%
  ungroup()
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Compute model results
# --- MODEL - CONSTRUCT --- #

# Define formula

formula = paste("get(response_variable_selected) ~",
                "ecosystem_type * disturbance * day +",
                "(day | culture_ID) +",
                "(day | baseline)") %>%
  print()
## [1] "get(response_variable_selected) ~ ecosystem_type * disturbance * day + (day | culture_ID) + (day | baseline)"
# Construct model

model = try.different.optimizers.ecos(data_for_analysis,
                                      formula)
## [1] "Model successfully fitted with optimizer: bobyqa "
# --- MODEL - SUMMARY --- #

print(summary(model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: formula
##    Data: data
## Control: lmerControl(optimizer = opt$optimizer)
## 
##      AIC      BIC   logLik deviance df.resid 
##  10359.9  10534.0  -5141.0  10281.9      602 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -4.3   -0.5    0.0    0.5    3.8 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 7e+03     83           
##             day         8e+01      9      -1.00
##  baseline   (Intercept) 4e+04    204           
##             day         5e+02     21      -1.00
##  Residual               5e+05    702           
## Number of obs: 641, groups:  culture_ID, 109; baseline, 109
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                             3e+03      4e+02  3e+02     8.9
## ecosystem_typeL_L                      -4e+02      5e+02  3e+02    -1.0
## ecosystem_typeL_S                       3e+02      5e+02  3e+02     0.5
## ecosystem_typeM                        -2e+01      5e+02  3e+02     0.0
## ecosystem_typeM_M                       7e+01      5e+02  3e+02     0.1
## ecosystem_typeS                        -1e+03      6e+02  3e+02    -2.1
## ecosystem_typeS_L                      -1e+03      5e+02  3e+02    -1.8
## ecosystem_typeS_S                      -1e+01      5e+02  3e+02     0.0
## disturbancelow                         -1e+02      5e+02  3e+02    -0.2
## day                                    -7e+00      2e+01  2e+02    -0.3
## ecosystem_typeL_L:disturbancelow       -4e+02      6e+02  3e+02    -0.6
## ecosystem_typeL_S:disturbancelow       -1e+03      7e+02  3e+02    -1.5
## ecosystem_typeM:disturbancelow          6e+01      7e+02  3e+02     0.1
## ecosystem_typeM_M:disturbancelow        6e+01      6e+02  3e+02     0.1
## ecosystem_typeS:disturbancelow          1e+03      8e+02  3e+02     1.5
## ecosystem_typeS_L:disturbancelow        9e+02      7e+02  3e+02     1.2
## ecosystem_typeS_S:disturbancelow       -2e+02      7e+02  3e+02    -0.3
## ecosystem_typeL_L:day                   6e+01      3e+01  2e+02     2.1
## ecosystem_typeL_S:day                  -3e-01      3e+01  2e+02     0.0
## ecosystem_typeM:day                     3e+01      3e+01  2e+02     1.0
## ecosystem_typeM_M:day                   2e+01      3e+01  2e+02     0.8
## ecosystem_typeS:day                     7e+01      4e+01  2e+02     1.9
## ecosystem_typeS_L:day                   9e+01      3e+01  2e+02     3.0
## ecosystem_typeS_S:day                  -4e+00      3e+01  2e+02    -0.1
## disturbancelow:day                      2e+01      3e+01  2e+02     0.8
## ecosystem_typeL_L:disturbancelow:day   -1e+00      4e+01  2e+02     0.0
## ecosystem_typeL_S:disturbancelow:day    5e+01      4e+01  2e+02     1.1
## ecosystem_typeM:disturbancelow:day     -2e+01      4e+01  2e+02    -0.6
## ecosystem_typeM_M:disturbancelow:day   -3e+01      4e+01  2e+02    -0.7
## ecosystem_typeS:disturbancelow:day     -6e+01      5e+01  2e+02    -1.3
## ecosystem_typeS_L:disturbancelow:day   -7e+01      4e+01  2e+02    -1.7
## ecosystem_typeS_S:disturbancelow:day    2e+01      4e+01  2e+02     0.6
##                                      Pr(>|t|)    
## (Intercept)                            <2e-16 ***
## ecosystem_typeL_L                       0.333    
## ecosystem_typeL_S                       0.584    
## ecosystem_typeM                         0.968    
## ecosystem_typeM_M                       0.882    
## ecosystem_typeS                         0.036 *  
## ecosystem_typeS_L                       0.067 .  
## ecosystem_typeS_S                       0.979    
## disturbancelow                          0.850    
## day                                     0.734    
## ecosystem_typeL_L:disturbancelow        0.535    
## ecosystem_typeL_S:disturbancelow        0.146    
## ecosystem_typeM:disturbancelow          0.933    
## ecosystem_typeM_M:disturbancelow        0.932    
## ecosystem_typeS:disturbancelow          0.146    
## ecosystem_typeS_L:disturbancelow        0.218    
## ecosystem_typeS_S:disturbancelow        0.802    
## ecosystem_typeL_L:day                   0.037 *  
## ecosystem_typeL_S:day                   0.993    
## ecosystem_typeM:day                     0.303    
## ecosystem_typeM_M:day                   0.423    
## ecosystem_typeS:day                     0.059 .  
## ecosystem_typeS_L:day                   0.003 ** 
## ecosystem_typeS_S:day                   0.895    
## disturbancelow:day                      0.417    
## ecosystem_typeL_L:disturbancelow:day    0.978    
## ecosystem_typeL_S:disturbancelow:day    0.257    
## ecosystem_typeM:disturbancelow:day      0.562    
## ecosystem_typeM_M:disturbancelow:day    0.485    
## ecosystem_typeS:disturbancelow:day      0.192    
## ecosystem_typeS_L:disturbancelow:day    0.099 .  
## ecosystem_typeS_S:disturbancelow:day    0.551    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# --- MODEL - ANOVA --- #

car::Anova(model, type = "III")
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: get(response_variable_selected)
##                                  Chisq Df Pr(>Chisq)    
## (Intercept)                    79.3960  1  < 2.2e-16 ***
## ecosystem_type                 13.9140  7   0.052733 .  
## disturbance                     0.0358  1   0.849879    
## day                             0.1156  1   0.733849    
## ecosystem_type:disturbance     12.4010  7   0.088118 .  
## ecosystem_type:day             20.7691  7   0.004127 ** 
## disturbance:day                 0.6627  1   0.415605    
## ecosystem_type:disturbance:day 13.0090  7   0.071889 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# --- ESTIMATE MARGINAL MEANS --- #

emmeans_output = emmeans(model,
                         specs = ~ ecosystem_type * disturbance * day,
                         adjust = "sidak",
                         bias.adj = TRUE,
                         lmer.df = "satterthwaite") 

emmeans_output
##  ecosystem_type disturbance  day emmean  SE  df lower.CL upper.CL
##  L              high        17.8   3207 155 126     2741     3672
##  L_L            high        17.8   3747 109 126     3418     4076
##  L_S            high        17.8   3492 155 126     3027     3958
##  M              high        17.8   3745 155 126     3280     4211
##  M_M            high        17.8   3651 109 126     3322     3980
##  S              high        17.8   3165 198 202     2574     3756
##  S_L            high        17.8   3853 155 126     3387     4318
##  S_S            high        17.8   3130 115 146     2784     3476
##  L              low         17.8   3547 155 126     3082     4012
##  L_L            low         17.8   3667 109 126     3338     3996
##  L_S            low         17.8   3614 155 126     3148     4079
##  M              low         17.8   3704 155 126     3238     4169
##  M_M            low         17.8   3583 109 126     3254     3912
##  S              low         17.8   3569 157 131     3098     4041
##  S_L            low         17.8   3849 155 126     3383     4314
##  S_S            low         17.8   3710 109 126     3380     4039
## 
## Degrees-of-freedom method: satterthwaite 
## Results are given on the get (not the response) scale. 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 16 estimates
# --- CODE EACH LEVEL OF DISTURBANCE AND ECOSYSTEM TYPE TO THEN PRODUCE CONTRASTS --- #

high_L = c(1, rep(0,15)) 
high_L_L = c(rep(0,1), 1, rep(0,14)) 
high_L_S = c(rep(0,2), 1, rep(0,13)) 
high_M = c(rep(0,3), 1, rep(0,12)) 
high_M_M = c(rep(0,4), 1, rep(0,11)) 
high_S = c(rep(0,5), 1, rep(0,10)) 
high_S_L = c(rep(0,6), 1, rep(0,9)) 
high_S_S = c(rep(0,7), 1, rep(0,8)) 
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
# --- PRODUCE ECOSYSTEM TYPE CONTRASTS --- #

# Set parameters

n_of_digits = 3

# Compute constrasts

contrasts = contrast(emmeans_output, 
                     method = list("high S_L - S" = high_S_L - high_S,
                                   "high S_L - S_S" = high_S_L - high_S_S,
                                   "high S_S - S" = high_S_S - high_S,
                                   "high M_M - M" = high_M_M - high_M,
                                   "high L_S - L" = high_L_S - high_L,
                                   "high L_S - L_L" = high_L_S - high_L_L,
                                   "high L_L - L" = high_L_L - high_L,
                                   "low S_L - S" = low_S_L - low_S,
                                   "low S_L - S_S" = low_S_L - low_S_S,
                                   "low S_S - S" = low_S_S - low_S,
                                   "low M_M - M" = low_M_M - low_M,
                                   "low L_S - L" = low_L_S - low_L,
                                   "low L_S - L_L" = low_L_S - low_L_L,
                                   "low L_L - L" = low_L_L - low_L)) %>%
  as.data.frame() %>%
  mutate(p.value = round(p.value, digits = n_of_digits),
         estimate = round(estimate, digits = n_of_digits),
         SE = round(SE, digits = n_of_digits),
         df = round(df, digits = n_of_digits),
         t.ratio = round(t.ratio, digits = n_of_digits),
         e = "",
         e = ifelse(p.value > 0.1, 
                           "",
                           e),
         e = ifelse(p.value < 0.05, 
                           "*",
                           e),
         e = ifelse(p.value < 0.01, 
                           "**",
                           e),
         e = ifelse(p.value < 0.001, 
                           "***",
                           e)) %>%
  rename(" " = e)
Show results
# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #

contrasts
##          contrast estimate      SE      df t.ratio p.value    
## 1    high S_L - S  687.553 251.380 167.153   2.735   0.007  **
## 2  high S_L - S_S  723.004 193.148 132.515   3.743   0.000 ***
## 3    high S_S - S  -35.451 229.229 185.647  -0.155   0.877    
## 4    high M_M - M  -93.928 189.642 125.539  -0.495   0.621    
## 5    high L_S - L  285.749 218.980 125.539   1.305   0.194    
## 6  high L_S - L_L -254.951 189.642 125.539  -1.344   0.181    
## 7    high L_L - L  540.699 189.642 125.539   2.851   0.005  **
## 8     low S_L - S  279.243 220.580 128.428   1.266   0.208    
## 9   low S_L - S_S  139.105 189.642 125.539   0.734   0.465    
## 10    low S_S - S  140.138 191.487 129.392   0.732   0.466    
## 11    low M_M - M -120.492 189.642 125.539  -0.635   0.526    
## 12    low L_S - L   66.693 218.980 125.539   0.305   0.761    
## 13  low L_S - L_L  -53.114 189.642 125.539  -0.280   0.780    
## 14    low L_L - L  119.807 189.642 125.539   0.632   0.529


Show model residuals residuals
# --- PLOT MODEL RESIDUALS --- #

# Simulate residuals from the fitted model

simulationOutput <- simulateResiduals(fittedModel = model, 
                                      n = 1000) 

# Test for overdispersion in the model to check if variance exceeds mean

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0018, p-value = 0.96
## alternative hypothesis: two.sided
# Plot Q-Q and Residuals vs Fitted plots

plot(simulationOutput)

Auto/Hetero

response_variable_selected = "auto_hetero_ratio"
Plot original data
# --- ORIGINAL DATA - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = ds_ecosystems %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
## Warning: Removed 2 rows containing non-finite outside the scale range
## (`stat_summary()`).
## Warning: Removed 2 rows containing non-finite outside the scale range
## (`stat_summary()`).
Prepare data for analysis
# --- PREPARE DATA FOR ANALYSIS --- #

# Add baselines

baselines = ds_ecosystems %>%
  filter(time_point == time_point_of_baselines) %>%
  select(culture_ID,
         all_of(response_variable_selected)) %>%
  rename(baseline = all_of(response_variable_selected))

data_for_analysis = ds_ecosystems %>%
  left_join(baselines)

# Filter data and change level names

data_for_analysis = data_for_analysis %>%
  filter(time_point %in% time_points_model,
         #!is.na(water_addition_ml),
         !is.na(!!sym(response_variable_selected)),
         !is.infinite(!!sym(response_variable_selected))) %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L",
                                    ecosystem_type == "Small connected to small" ~ "S_S",
                                    ecosystem_type == "Small connected to large" ~ "S_L",
                                    ecosystem_type == "Medium connected to medium" ~ "M_M",
                                    ecosystem_type == "Large connected to large" ~ "L_L",
                                    ecosystem_type == "Large connected to small" ~ "L_S",
                                    TRUE ~ ecosystem_type)) %>%
  ungroup()
Plot data for analysis means
# --- DATA FOR ANALYSIS - PLOT MEAN ± 95% CI --- #

p1 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "high"),
                             response_variable_selected) +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "High disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") + # Adjust position and style
  theme(axis.title.x = element_blank(),  # Remove x-axis title
        axis.text.x = element_blank())  # Remove x-axis text
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p2 = plot.all.patches.points(data = data_for_analysis %>% 
                               filter(disturbance == "low"),
                             response_variable_selected) +
  theme(legend.position = "none") +
  annotate("text", 
           x = Inf, 
           y = Inf, 
           label = "Low disturbance", 
           hjust = 1.1, 
           vjust = 1.1, 
           size = 5, 
           fontface = "bold") # Adjust position and style

# Arrange the plots vertically

ggarrange(p1, 
          p2, 
          ncol = 1, 
          nrow = 2, 
          heights = c(1, 0.7))
Compute model results
# --- MODEL - CONSTRUCT --- #

# Define formula

formula = paste("get(response_variable_selected) ~",
                "ecosystem_type * disturbance * day +",
                "(day | culture_ID) +",
                "(day | baseline)") %>%
  print()
## [1] "get(response_variable_selected) ~ ecosystem_type * disturbance * day + (day | culture_ID) + (day | baseline)"
# Construct model

model = try.different.optimizers.ecos(data_for_analysis,
                                      formula)
## [1] "Model successfully fitted with optimizer: bobyqa "
# --- MODEL - SUMMARY --- #

print(summary(model), digits = 1)
## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
##   method [lmerModLmerTest]
## Formula: formula
##    Data: data
## Control: lmerControl(optimizer = opt$optimizer)
## 
##      AIC      BIC   logLik deviance df.resid 
##   -447.3   -273.4    262.7   -525.3      600 
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
##   -3.5   -0.5   -0.1    0.3    8.0 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev. Corr 
##  culture_ID (Intercept) 1e-09    3e-05         
##             day         6e-12    2e-06    -1.00
##  baseline   (Intercept) 1e-02    1e-01         
##             day         9e-05    9e-03    -1.00
##  Residual               2e-02    1e-01         
## Number of obs: 639, groups:  culture_ID, 109; baseline, 104
## 
## Fixed effects:
##                                      Estimate Std. Error     df t value
## (Intercept)                            -2e-01      9e-02  2e+02    -1.7
## ecosystem_typeL_L                       2e-01      1e-01  2e+02     1.9
## ecosystem_typeL_S                       1e-01      1e-01  2e+02     0.9
## ecosystem_typeM                         2e-01      1e-01  2e+02     1.7
## ecosystem_typeM_M                       1e-01      1e-01  2e+02     1.2
## ecosystem_typeS                         3e-01      1e-01  2e+02     2.2
## ecosystem_typeS_L                       4e-01      1e-01  2e+02     2.9
## ecosystem_typeS_S                       3e-01      1e-01  2e+02     3.0
## disturbancelow                          4e-01      1e-01  2e+02     3.1
## day                                     2e-02      6e-03  1e+02     4.1
## ecosystem_typeL_L:disturbancelow       -4e-01      2e-01  2e+02    -2.6
## ecosystem_typeL_S:disturbancelow       -3e-01      2e-01  2e+02    -1.8
## ecosystem_typeM:disturbancelow         -4e-01      2e-01  2e+02    -2.4
## ecosystem_typeM_M:disturbancelow       -4e-01      2e-01  2e+02    -2.4
## ecosystem_typeS:disturbancelow         -5e-01      2e-01  2e+02    -2.7
## ecosystem_typeS_L:disturbancelow       -6e-01      2e-01  2e+02    -3.1
## ecosystem_typeS_S:disturbancelow       -6e-01      2e-01  2e+02    -3.7
## ecosystem_typeL_L:day                  -2e-02      7e-03  1e+02    -2.7
## ecosystem_typeL_S:day                  -8e-03      8e-03  1e+02    -1.0
## ecosystem_typeM:day                    -2e-02      8e-03  1e+02    -2.7
## ecosystem_typeM_M:day                  -1e-02      7e-03  1e+02    -1.9
## ecosystem_typeS:day                    -3e-02      9e-03  1e+02    -3.3
## ecosystem_typeS_L:day                  -3e-02      8e-03  2e+02    -3.9
## ecosystem_typeS_S:day                  -3e-02      7e-03  1e+02    -4.5
## disturbancelow:day                     -3e-02      8e-03  1e+02    -3.5
## ecosystem_typeL_L:disturbancelow:day    3e-02      1e-02  1e+02     3.1
## ecosystem_typeL_S:disturbancelow:day    2e-02      1e-02  1e+02     1.7
## ecosystem_typeM:disturbancelow:day      4e-02      1e-02  1e+02     3.1
## ecosystem_typeM_M:disturbancelow:day    3e-02      1e-02  1e+02     2.7
## ecosystem_typeS:disturbancelow:day      4e-02      1e-02  1e+02     3.2
## ecosystem_typeS_L:disturbancelow:day    4e-02      1e-02  2e+02     3.3
## ecosystem_typeS_S:disturbancelow:day    4e-02      1e-02  1e+02     4.2
##                                      Pr(>|t|)    
## (Intercept)                             0.098 .  
## ecosystem_typeL_L                       0.056 .  
## ecosystem_typeL_S                       0.375    
## ecosystem_typeM                         0.095 .  
## ecosystem_typeM_M                       0.228    
## ecosystem_typeS                         0.030 *  
## ecosystem_typeS_L                       0.004 ** 
## ecosystem_typeS_S                       0.003 ** 
## disturbancelow                          0.002 ** 
## day                                     7e-05 ***
## ecosystem_typeL_L:disturbancelow        0.009 ** 
## ecosystem_typeL_S:disturbancelow        0.070 .  
## ecosystem_typeM:disturbancelow          0.016 *  
## ecosystem_typeM_M:disturbancelow        0.016 *  
## ecosystem_typeS:disturbancelow          0.008 ** 
## ecosystem_typeS_L:disturbancelow        0.002 ** 
## ecosystem_typeS_S:disturbancelow        2e-04 ***
## ecosystem_typeL_L:day                   0.007 ** 
## ecosystem_typeL_S:day                   0.298    
## ecosystem_typeM:day                     0.008 ** 
## ecosystem_typeM_M:day                   0.066 .  
## ecosystem_typeS:day                     0.001 ** 
## ecosystem_typeS_L:day                   1e-04 ***
## ecosystem_typeS_S:day                   2e-05 ***
## disturbancelow:day                      6e-04 ***
## ecosystem_typeL_L:disturbancelow:day    0.002 ** 
## ecosystem_typeL_S:disturbancelow:day    0.093 .  
## ecosystem_typeM:disturbancelow:day      0.003 ** 
## ecosystem_typeM_M:disturbancelow:day    0.008 ** 
## ecosystem_typeS:disturbancelow:day      0.002 ** 
## ecosystem_typeS_L:disturbancelow:day    0.001 ** 
## ecosystem_typeS_S:disturbancelow:day    4e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# --- MODEL - ANOVA --- #

car::Anova(model, type = "III")
## Analysis of Deviance Table (Type III Wald chisquare tests)
## 
## Response: get(response_variable_selected)
##                                  Chisq Df Pr(>Chisq)    
## (Intercept)                     2.7670  1   0.096224 .  
## ecosystem_type                 15.6134  7   0.028893 *  
## disturbance                     9.6489  1   0.001895 ** 
## day                            17.0660  1  3.610e-05 ***
## ecosystem_type:disturbance     16.4222  7   0.021527 *  
## ecosystem_type:day             32.9062  7  2.756e-05 ***
## disturbance:day                12.3798  1   0.000434 ***
## ecosystem_type:disturbance:day 22.2662  7   0.002285 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# --- ESTIMATE MARGINAL MEANS --- #

emmeans_output = emmeans(model,
                         specs = ~ ecosystem_type * disturbance * day,
                         adjust = "sidak",
                         bias.adj = TRUE,
                         lmer.df = "satterthwaite") 

emmeans_output
##  ecosystem_type disturbance  day emmean     SE  df lower.CL upper.CL
##  L              high        17.8 0.2681 0.0349 135  0.16348    0.373
##  L_L            high        17.8 0.1483 0.0238 182  0.07714    0.219
##  L_S            high        17.8 0.2331 0.0349 135  0.12846    0.338
##  M              high        17.8 0.0943 0.0349 135 -0.01038    0.199
##  M_M            high        17.8 0.1727 0.0247 135  0.09868    0.247
##  S              high        17.8 0.0432 0.0439 202 -0.08773    0.174
##  S_L            high        17.8 0.1013 0.0330 251  0.00313    0.199
##  S_S            high        17.8 0.0389 0.0255 196 -0.03734    0.115
##  L              low         17.8 0.1648 0.0349 135  0.06019    0.269
##  L_L            low         17.8 0.1655 0.0238 182  0.09432    0.237
##  L_S            low         17.8 0.1403 0.0349 135  0.03565    0.245
##  M              low         17.8 0.1682 0.0349 135  0.06355    0.273
##  M_M            low         17.8 0.1581 0.0238 182  0.08700    0.229
##  S              low         17.8 0.1202 0.0354 141  0.01408    0.226
##  S_L            low         17.8 0.0773 0.0327 236 -0.01993    0.175
##  S_S            low         17.8 0.0918 0.0247 135  0.01782    0.166
## 
## Degrees-of-freedom method: satterthwaite 
## Results are given on the get (not the response) scale. 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 16 estimates
# --- CODE EACH LEVEL OF DISTURBANCE AND ECOSYSTEM TYPE TO THEN PRODUCE CONTRASTS --- #

high_L = c(1, rep(0,15)) 
high_L_L = c(rep(0,1), 1, rep(0,14)) 
high_L_S = c(rep(0,2), 1, rep(0,13)) 
high_M = c(rep(0,3), 1, rep(0,12)) 
high_M_M = c(rep(0,4), 1, rep(0,11)) 
high_S = c(rep(0,5), 1, rep(0,10)) 
high_S_L = c(rep(0,6), 1, rep(0,9)) 
high_S_S = c(rep(0,7), 1, rep(0,8)) 
low_L = c(rep(0,8), 1, rep(0,7))
low_L_L = c(rep(0,9), 1, rep(0,6))
low_L_S = c(rep(0,10), 1, rep(0,5))
low_M = c(rep(0,11), 1, rep(0,4))
low_M_M = c(rep(0,12), 1, rep(0,3))
low_S = c(rep(0,13), 1, rep(0,2))
low_S_L = c(rep(0,14), 1, rep(0,1))
low_S_S = c(rep(0,15), 1)
# --- PRODUCE ECOSYSTEM TYPE CONTRASTS --- #

# Set parameters

n_of_digits = 3

# Compute constrasts

contrasts = contrast(emmeans_output, 
         method = list("high L - S" = high_L - high_S,
                       "high M - S" = high_M - high_S,
                       "low L - S" = low_L - low_S,
                       "low M - S" = low_M - low_S)) %>%
  as.data.frame() %>%
  mutate(p.value = round(p.value, digits = n_of_digits),
         estimate = round(estimate, digits = n_of_digits),
         SE = round(SE, digits = n_of_digits),
         df = round(df, digits = n_of_digits),
         t.ratio = round(t.ratio, digits = n_of_digits),
         e = "",
         e = ifelse(p.value > 0.1, 
                           "",
                           e),
         e = ifelse(p.value < 0.05, 
                           "*",
                           e),
         e = ifelse(p.value < 0.01, 
                           "**",
                           e),
         e = ifelse(p.value < 0.001, 
                           "***",
                           e)) %>%
  rename(" " = e)
Show results
# --- SHOW ECOSYSTEM TYPE CONSTRASTS --- #

contrasts
##     contrast estimate    SE      df t.ratio p.value    
## 1 high L - S    0.225 0.056 172.002   4.013   0.000 ***
## 2 high M - S    0.051 0.056 172.002   0.911   0.364    
## 3  low L - S    0.045 0.050 137.957   0.899   0.370    
## 4  low M - S    0.048 0.050 137.957   0.967   0.335


Show model residuals residuals
# --- PLOT MODEL RESIDUALS --- #

# Simulate residuals from the fitted model

simulationOutput <- simulateResiduals(fittedModel = model, 
                                      n = 1000) 

# Test for overdispersion in the model to check if variance exceeds mean

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.99756, p-value = 0.998
## alternative hypothesis: two.sided
# Plot Q-Q and Residuals vs Fitted plots

plot(simulationOutput)

BEF

# --- PLOT BIOMASS-SPECIES RICHNESS RELATIONSHIP --- #

ds_ecosystems %>%
    filter(is.na(species_richness) != TRUE) %>%
    ggplot(aes(x = species_richness,
               y = bioarea_mm2_per_ml)) +
    geom_point() +
    xlim(0, length(protist_species)) +
    labs(x = axis_names$axis_name[axis_names$variable == "species_richness"],
         y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) + 
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm"))

# --- PLOT BIOMASS-SHANNON RELATIONSHIP --- #

ds_ecosystems %>%
  filter(is.na(shannon) != TRUE) %>%
  ggplot(aes(x = shannon,
             y = bioarea_mm2_per_ml)) +
  geom_point() +
  labs(x = axis_names$axis_name[axis_names$variable == "shannon"],
       y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) + 
  theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm"))

# --- PLOT BIOMASS-EVENESS RELATIONSHIP --- #

ds_ecosystems %>%
  filter(is.na(evenness_pielou) != TRUE) %>%
  ggplot(aes(x = evenness_pielou,
             y = bioarea_mm2_per_ml)) +
  geom_point() +
  labs(x = axis_names$axis_name[axis_names$variable == "evenness_pielou"],
       y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) + 
  theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm"))

Populations

Figures

High disturbance

disturbance_selected = "high"
# --- PREPARE DATA FOR PLOTTING --- #

# Define what you want to plot

metaecosystem_type_selected = c("Medium-Medium",
                                "Small-Large")

# Filter dataset

data_for_plotting = ds_metaecosystems %>%
  filter(metaecosystem_type %in% metaecosystem_type_selected,
         disturbance == disturbance_selected)
# Write function to plot a response variable. Afterwards you can use this function to plot alpha, beta, gamma diversity, and biomass.

plot.single.plot = function(response_variable_selected){
  
  data_for_plotting %>%
    filter(metaecosystem_type %in% metaecosystem_type_selected,
           !is.na(!!sym(response_variable_selected))) %>%
    summarySE(measurevar = response_variable_selected,
              groupvars = c("day", "ecosystem_size_symmetry", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable_selected),
               group = interaction(day, ecosystem_size_symmetry, connection),
               color = ecosystem_size_symmetry,
               linetype = connection)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = interaction(ecosystem_size_symmetry, connection)),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
                      ymin = get(response_variable_selected) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable_selected],
         color = "") +
    scale_color_manual(values = treatment_colours_paper) +
    scale_linetype_manual(values = treatment_linetype_paper) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 2),
           linetype = guide_legend(title = NULL,
                                   nrow = 2)) +
    theme(plot.margin = unit(c(ggarrange_margin_left,
                               ggarrange_margin_right,
                               ggarrange_margin_bottom,
                               ggarrange_margin_left),
                             "cm")) +
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# Combine plots of alpha, beta, gamma biodiversity and biomass.

p_combined = ggarrange(plot.single.plot("mean_shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", size = paper_labels_size) +
                         font("ylab", size = paper_labels_size),
                       plot.single.plot("bray_curtis") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("metaecosystem_richness") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("total_metaecosystem_bioarea_mm2") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(data_for_plotting$day)),
                       heights = c(0.8, 0.8, 0.8, 1),
                       nrow = 4,
                       common.legend = TRUE,
                       align = "v",
                       labels = c("(a)", "(b)", "(c)", "(d)"),
                       label.x = 0.1,
                       label.y = 0.8) %>%
  print()

# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_selected = c("Small connected to large",
                            "Small connected to small",
                            "Small unconnected",
                            "Large connected to small",
                            "Large connected to large",
                            "Large unconnected")

# Filter data

data_for_plotting = ds_ecosystems %>%
  filter(ecosystem_type %in% ecosystem_type_selected,
         disturbance == disturbance_selected)
# --- CONSTRUCT FUNCTION TO PLOT BIOMASS/SHANNON OF SMALL AND LARGE ECOSYSTEMS --- #

plot.single.plot = function(response_variable_selected){
  
  data_for_plotting %>%
    filter(!is.na(!!sym(response_variable_selected))) %>%
    summarySE(measurevar = response_variable_selected,
              groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable_selected),
               group = interaction(day, ecosystem_type),
               color = ecosystem_type,
               linetype = ecosystem_type)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = ecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
                      ymin = get(response_variable_selected) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable_selected],
         color = "") +
    scale_color_manual(values = c("#993404",
                                  "#993404",
                                  "#993404",
                                  "#3182bd",
                                  "#3182bd",
                                  "#3182bd"),
                       label = expression(S[L], 
                                          S[S],
                                          S,
                                          L[S], 
                                          L[L], 
                                          L)) +
    scale_linetype_manual(values = c("solid",
                                     "dashed",
                                     "dotted",
                                     "solid",
                                     "dashed",
                                     "dotted"),
                          label = expression(S[L], 
                                             S[S],
                                             S,
                                             L[S], 
                                             L[L], 
                                             L)) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    geom_hline(yintercept = 0,
               color = zero_line_colour,
               linetype = zero_line_line_type,
               linewidth = zero_line_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 3),
           linetype = guide_legend(title = NULL,
                                   nrow = 3)) + 
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# --- COMBINE PLOTS OF SHANNON AND BIOMASS --- #

p_combined = ggarrange(plot.single.plot("shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("bioarea_mm2_per_ml") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(data_for_plotting$day)),
                       heights = c(0.8, 0.8, 1),
                       nrow = 2,
                       align = "v",
                       labels = c("(a)", "(b)"),
                       label.x = 0.1,
                       label.y = 0.8,
                       common.legend = TRUE) %>%
  print()
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced

# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_selected = c("Medium connected to medium",
                            "Medium unconnected")

# Filter data

data_for_plotting = ds_ecosystems %>%
  filter(ecosystem_type %in% ecosystem_type_selected,
         disturbance == disturbance_selected,
         !is.na(!!sym(response_variable_selected)))
# --- CONSTRUCT FUNCTION TO PLOT BIOMASS/SHANNON OF MEDIUM ECOSYSTEMS --- #

plot.single.plot = function(response_variable_selected){
  
  data_for_plotting %>%
    summarySE(measurevar = response_variable_selected,
              groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable_selected),
               group = interaction(day, ecosystem_type),
               color = ecosystem_type,
               linetype = ecosystem_type)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = ecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
                      ymin = get(response_variable_selected) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable_selected],
         color = "") +
    scale_color_manual(values = c("#d95f0e",
                                  "#d95f0e"),
                       label = expression(M[M], 
                                          M)) +
    scale_linetype_manual(values = c("dashed",
                                     "dotted"),
                          label = expression(M[M], 
                                             M)) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    geom_hline(yintercept = 0,
               color = zero_line_colour,
               linetype = zero_line_line_type,
               linewidth = zero_line_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 3),
           linetype = guide_legend(title = NULL,
                                   nrow = 3)) + 
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# --- COMBINE PLOTS OF SHANNON AND BIOMASS --- #

p_combined = ggarrange(plot.single.plot("shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("bioarea_mm2_per_ml") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(data_for_plotting$day)),
                       heights = c(0.8, 0.8, 1),
                       nrow = 2,
                       align = "v",
                       labels = c("(a)", "(b)"),
                       label.x = 0.1,
                       label.y = 0.8,
                       common.legend = TRUE) %>%
  print()

# --- DEFINE RESPONSE VARIABLE YOU WANT TO PLOT --- #

response_variable = "auto_hetero_ratio"
# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_selected = c("S",
                            "M",
                            "L")

# Manipulate data

data_for_plotting = ds_ecosystems %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L")) %>%
  filter(ecosystem_type %in% ecosystem_type_selected,
         disturbance == disturbance_selected,
         !is.na(!!sym(response_variable)))
# --- CONSTRUCT PLOT --- #

p = data_for_plotting %>%
  
  # Manipulate
  
  summarySE(measurevar = response_variable,
            groupvars = c("day", "ecosystem_type", "ecosystem_size", "connection")) %>%
  
  # Create plot
  
  ggplot(aes(x = day,
             y = get(response_variable),
             group = interaction(day, ecosystem_type),
             color = ecosystem_type)) +
  
  # Points
  
  geom_point(stat = "summary",
             fun = "mean",
             position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_errorbar(aes(ymax = get(response_variable) + ci,
                    ymin = get(response_variable) - ci),
                width = width_errorbar,
                position = position_dodge(dodging)) +
  
  # Lines
  
  geom_line(stat = "summary",
            fun = "mean",
            aes(group = ecosystem_type),
            position = position_dodge(dodging),
            linewidth = treatment_lines_linewidth) +
  
  # Axes and legend
  
  labs(x = axis_names$axis_name[axis_names$variable == "day"],
       y = axis_names$axis_name[axis_names$variable == response_variable],
       color = "") +
  scale_x_continuous(breaks = unique(data_for_plotting$day)) +
  guides(color = guide_legend(title = NULL,
                              nrow = 1),
         linetype = guide_legend(title = NULL,
                                 nrow = 1)) +
  scale_color_manual(values = c("#000000",
                                "#737373",
                                "#bdbdbd")) +
  
  # Extra graphic elements
  
  theme_bw() +
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        legend.position = legend_position,
        legend.key.width = unit(legend_width_cm, "cm"),
        axis.title.x = element_text(size = paper_labels_size),
        axis.title.y = element_text(size = paper_labels_size),
        legend.text = element_text(size = paper_labels_size)) +
  geom_rect(xmin = grey_background_xmin, 
            xmax = grey_background_xmax,
            ymin = grey_background_ymin, 
            ymax = grey_background_ymax, 
            fill = grey_background_fill, 
            alpha = grey_background_alpha,
            color = grey_background_color) + 
  geom_hline(yintercept = 0,
             color = zero_line_colour,
             linetype = zero_line_line_type,
             linewidth = zero_line_line_width) +
  
  geom_vline(xintercept = resource_flow_days,
             linetype = resource_flow_line_type,
             color = resource_flow_line_colour,
             linewidth = resource_flow_line_width)
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
p

Figures to present
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
# --- DEFINE PLOTTING PARAMETERS --- #

legend_row_n_input = 2
size_y_axis = 22
x_min = -0.2
x_max = 30
y_min = -0.8
y_max = 3
# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_all = c("Small connected to large",
                       "Small unconnected",
                       "Small connected to small",
                       "Large connected to small",
                       "Large unconnected",
                       "Large connected to large")

response_variable_selected = "shannon"

# Filter data

data_for_plotting = ds_ecosystems %>%
  filter(ecosystem_type %in% ecosystem_type_all,
         disturbance == disturbance_selected)
# --- CONSTRUCT PLOTS --- #

# Define parameters

plots = NULL

# Construct plots

plots[[1]] = plot.ecosystems.empty.presentations(y_min_alpha,
                                                 y_max_alpha,
                                                 "shannon")

for (i in 1:length(ecosystem_type_all)+1) {
  
  plots[[i+1]] = plot.ecosystems.points.presentations(data = data_for_plotting,
                                                      ecosystem_type_selected = ecosystem_type_all[1:i],
                                                      response_variable_selected) +
    theme(plot.margin = unit(c(ggarrange_margin_left,
                               ggarrange_margin_right,
                               ggarrange_margin_bottom,
                               ggarrange_margin_left),
                             "cm"),
          legend.position = "none") +
    scale_y_continuous(labels = scales::number_format(accuracy = 0.01)) + 
    xlim(x_min, x_max) +
    ylim(y_min, y_max)
  
  }
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
# --- COMBINE PLOTS --- #

# Define parameters

p_combined = NULL
p_combined[[1]] = plots[[1]]

# Combine plots

for(i in 1:length(ecosystem_type_all)+1){
  
  p_combined[[i]] = ggarrange(plots[[i]] +
                                theme(axis.text = element_text(size = presentation_axes_size)) + 
                                font("legend.text", size = size_legend) +
                                font("xlab", size = size_y_axis) +
                                font("ylab", size = size_y_axis),
                              nrow = 1,
                              align = "v",
                              label.x = 0.1,
                              label.y = 0.8)

  }
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).
# --- SAVE COMBINED PLOTS --- #

for(i in 1:length(ecosystem_type_all)+1){
  
  png(file = here("3_results", 
                  "figures", 
                  disturbance_selected, 
                  "presentations", 
                  paste0("ecosystems_connected_diversity_", i, ".png")),
      width = presentation_figure_width,
      height = presentation_figure_height,
      units = presentation_figure_units,
      res = presentation_figure_res)
  
  print(p_combined[[i]])
  
  dev.off()
  
  }

Low disturbance

disturbance_selected = "low"
# --- PREPARE DATA FOR PLOTTING --- #

# Define what you want to plot

metaecosystem_type_selected = c("Medium-Medium",
                                "Small-Large")

# Filter dataset

data_for_plotting = ds_metaecosystems %>%
  filter(metaecosystem_type %in% metaecosystem_type_selected,
         disturbance == disturbance_selected)
# Write function to plot a response variable. Afterwards you can use this function to plot alpha, beta, gamma diversity, and biomass.

plot.single.plot = function(response_variable_selected){
  
  data_for_plotting %>%
    filter(metaecosystem_type %in% metaecosystem_type_selected,
           !is.na(!!sym(response_variable_selected))) %>%
    summarySE(measurevar = response_variable_selected,
              groupvars = c("day", "ecosystem_size_symmetry", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable_selected),
               group = interaction(day, ecosystem_size_symmetry, connection),
               color = ecosystem_size_symmetry,
               linetype = connection)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = interaction(ecosystem_size_symmetry, connection)),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
                      ymin = get(response_variable_selected) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable_selected],
         color = "") +
    scale_color_manual(values = treatment_colours_paper) +
    scale_linetype_manual(values = treatment_linetype_paper) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 2),
           linetype = guide_legend(title = NULL,
                                   nrow = 2)) +
    theme(plot.margin = unit(c(ggarrange_margin_left,
                               ggarrange_margin_right,
                               ggarrange_margin_bottom,
                               ggarrange_margin_left),
                             "cm")) +
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# Combine plots of alpha, beta, gamma biodiversity and biomass.

p_combined = ggarrange(plot.single.plot("mean_shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", size = paper_labels_size) +
                         font("ylab", size = paper_labels_size),
                       plot.single.plot("bray_curtis") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("metaecosystem_richness") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("total_metaecosystem_bioarea_mm2") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(data_for_plotting$day)),
                       heights = c(0.8, 0.8, 0.8, 1),
                       nrow = 4,
                       common.legend = TRUE,
                       align = "v",
                       labels = c("(a)", "(b)", "(c)", "(d)"),
                       label.x = 0.1,
                       label.y = 0.8) %>%
  print()

# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_selected = c("Small connected to large",
                            "Small connected to small",
                            "Small unconnected",
                            "Large connected to small",
                            "Large connected to large",
                            "Large unconnected")

# Filter data

data_for_plotting = ds_ecosystems %>%
  filter(ecosystem_type %in% ecosystem_type_selected,
         disturbance == disturbance_selected)
# --- CONSTRUCT FUNCTION TO PLOT BIOMASS/SHANNON OF SMALL AND LARGE ECOSYSTEMS --- #

plot.single.plot = function(response_variable_selected){
  
  data_for_plotting %>%
    filter(!is.na(!!sym(response_variable_selected))) %>%
    summarySE(measurevar = response_variable_selected,
              groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable_selected),
               group = interaction(day, ecosystem_type),
               color = ecosystem_type,
               linetype = ecosystem_type)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = ecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
                      ymin = get(response_variable_selected) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable_selected],
         color = "") +
    scale_color_manual(values = c("#993404",
                                  "#993404",
                                  "#993404",
                                  "#3182bd",
                                  "#3182bd",
                                  "#3182bd"),
                       label = expression(S[L], 
                                          S[S],
                                          S,
                                          L[S], 
                                          L[L], 
                                          L)) +
    scale_linetype_manual(values = c("solid",
                                     "dashed",
                                     "dotted",
                                     "solid",
                                     "dashed",
                                     "dotted"),
                          label = expression(S[L], 
                                             S[S],
                                             S,
                                             L[S], 
                                             L[L], 
                                             L)) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    geom_hline(yintercept = 0,
               color = zero_line_colour,
               linetype = zero_line_line_type,
               linewidth = zero_line_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 3),
           linetype = guide_legend(title = NULL,
                                   nrow = 3)) + 
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# --- COMBINE PLOTS OF SHANNON AND BIOMASS --- #

p_combined = ggarrange(plot.single.plot("shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("bioarea_mm2_per_ml") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(data_for_plotting$day)),
                       heights = c(0.8, 0.8, 1),
                       nrow = 2,
                       align = "v",
                       labels = c("(a)", "(b)"),
                       label.x = 0.1,
                       label.y = 0.8,
                       common.legend = TRUE) %>%
  print()

# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_selected = c("Medium connected to medium",
                            "Medium unconnected")

# Filter data

data_for_plotting = ds_ecosystems %>%
  filter(ecosystem_type %in% ecosystem_type_selected,
         disturbance == disturbance_selected,
         !is.na(!!sym(response_variable_selected)))
# --- CONSTRUCT FUNCTION TO PLOT BIOMASS/SHANNON OF MEDIUM ECOSYSTEMS --- #

plot.single.plot = function(response_variable_selected){
  
  data_for_plotting %>%
    summarySE(measurevar = response_variable_selected,
              groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
    ggplot(aes(x = day,
               y = get(response_variable_selected),
               group = interaction(day, ecosystem_type),
               color = ecosystem_type,
               linetype = ecosystem_type)) +
    geom_point(stat = "summary",
               fun = "mean",
               position = position_dodge(dodging),
               size = treatment_points_size) +
    geom_line(stat = "summary",
              fun = "mean",
              aes(group = ecosystem_type),
              position = position_dodge(dodging),
              linewidth = treatment_lines_linewidth) +
    geom_errorbar(aes(ymax = get(response_variable_selected) + ci,
                      ymin = get(response_variable_selected) - ci),
                  width = width_errorbar,
                  position = position_dodge(dodging)) +
    labs(x = axis_names$axis_name[axis_names$variable == "day"],
         y = axis_names$axis_name[axis_names$variable == response_variable_selected],
         color = "") +
    scale_color_manual(values = c("#d95f0e",
                                  "#d95f0e"),
                       label = expression(M[M], 
                                          M)) +
    scale_linetype_manual(values = c("dashed",
                                     "dotted"),
                          label = expression(M[M], 
                                             M)) +
    geom_vline(xintercept = resource_flow_days,
               linetype = resource_flow_line_type,
               color = resource_flow_line_colour,
               linewidth = resource_flow_line_width) +
    geom_hline(yintercept = 0,
               color = zero_line_colour,
               linetype = zero_line_line_type,
               linewidth = zero_line_line_width) +
    theme_bw() +
    theme(panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          legend.position = legend_position,
          legend.key.width = unit(legend_width_cm, "cm")) +
    guides(color = guide_legend(title = NULL,
                                nrow = 3),
           linetype = guide_legend(title = NULL,
                                   nrow = 3)) + 
    geom_rect(xmin = grey_background_xmin, 
              xmax = grey_background_xmax,
              ymin = grey_background_ymin, 
              ymax = grey_background_ymax, 
              fill = grey_background_fill, 
              alpha = grey_background_alpha,
              color = grey_background_color)
}
# --- COMBINE PLOTS OF SHANNON AND BIOMASS --- #

p_combined = ggarrange(plot.single.plot("shannon") +
                         rremove("xlab") +
                         theme(axis.text.x = element_blank(),
                               axis.ticks.x = element_blank()) +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size),
                       plot.single.plot("bioarea_mm2_per_ml") +
                         font("legend.text", 
                              size = paper_labels_size) +
                         font("xlab", 
                              size = paper_labels_size) +
                         font("ylab", 
                              size = paper_labels_size) +
                         scale_x_continuous(breaks = unique(data_for_plotting$day)),
                       heights = c(0.8, 0.8, 1),
                       nrow = 2,
                       align = "v",
                       labels = c("(a)", "(b)"),
                       label.x = 0.1,
                       label.y = 0.8,
                       common.legend = TRUE) %>%
  print()

# --- DEFINE RESPONSE VARIABLE YOU WANT TO PLOT --- #

response_variable = "auto_hetero_ratio"
# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_selected = c("S",
                            "M",
                            "L")

# Manipulate data

data_for_plotting = ds_ecosystems %>%
  mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
                                    ecosystem_type == "Medium unconnected" ~ "M",
                                    ecosystem_type == "Large unconnected" ~ "L")) %>%
  filter(ecosystem_type %in% ecosystem_type_selected,
         disturbance == disturbance_selected,
         !is.na(!!sym(response_variable)))
# --- CONSTRUCT PLOT --- #

p = data_for_plotting %>%
  
  # Manipulate
  
  summarySE(measurevar = response_variable,
            groupvars = c("day", "ecosystem_type", "ecosystem_size", "connection")) %>%
  
  # Create plot
  
  ggplot(aes(x = day,
             y = get(response_variable),
             group = interaction(day, ecosystem_type),
             color = ecosystem_type)) +
  
  # Points
  
  geom_point(stat = "summary",
             fun = "mean",
             position = position_dodge(dodging),
             size = treatment_points_size) +
  geom_errorbar(aes(ymax = get(response_variable) + ci,
                    ymin = get(response_variable) - ci),
                width = width_errorbar,
                position = position_dodge(dodging)) +
  
  # Lines
  
  geom_line(stat = "summary",
            fun = "mean",
            aes(group = ecosystem_type),
            position = position_dodge(dodging),
            linewidth = treatment_lines_linewidth) +
  
  # Axes and legend
  
  labs(x = axis_names$axis_name[axis_names$variable == "day"],
       y = axis_names$axis_name[axis_names$variable == response_variable],
       color = "") +
  scale_x_continuous(breaks = unique(data_for_plotting$day)) +
  guides(color = guide_legend(title = NULL,
                              nrow = 1),
         linetype = guide_legend(title = NULL,
                                 nrow = 1)) +
  scale_color_manual(values = c("#000000",
                                "#737373",
                                "#bdbdbd")) +
  
  # Extra graphic elements
  
  theme_bw() +
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        legend.position = legend_position,
        legend.key.width = unit(legend_width_cm, "cm"),
        axis.title.x = element_text(size = paper_labels_size),
        axis.title.y = element_text(size = paper_labels_size),
        legend.text = element_text(size = paper_labels_size)) +
  geom_rect(xmin = grey_background_xmin, 
            xmax = grey_background_xmax,
            ymin = grey_background_ymin, 
            ymax = grey_background_ymax, 
            fill = grey_background_fill, 
            alpha = grey_background_alpha,
            color = grey_background_color) + 
  geom_hline(yintercept = 0,
             color = zero_line_colour,
             linetype = zero_line_line_type,
             linewidth = zero_line_line_width) +
  
  geom_vline(xintercept = resource_flow_days,
             linetype = resource_flow_line_type,
             color = resource_flow_line_colour,
             linewidth = resource_flow_line_width)

p

Figures to present
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# --- DEFINE PLOTTING PARAMETERS --- #

legend_row_n_input = 2
size_y_axis = 22
x_min = -0.2
x_max = 30
y_min = -0.8
y_max = 3
# --- PREPARE DATA FOR PLOTTING --- #

# Define parameters

ecosystem_type_all = c("Small connected to large",
                       "Small unconnected",
                       "Small connected to small",
                       "Large connected to small",
                       "Large unconnected",
                       "Large connected to large")

response_variable_selected = "shannon"

# Filter data

data_for_plotting = ds_ecosystems %>%
  filter(ecosystem_type %in% ecosystem_type_all,
         disturbance == disturbance_selected)
# --- CONSTRUCT PLOTS --- #

# Define parameters

plots = NULL

# Construct plots

plots[[1]] = plot.ecosystems.empty.presentations(y_min_alpha,
                                                 y_max_alpha,
                                                 "shannon")

for (i in 1:length(ecosystem_type_all)+1) {
  
  plots[[i+1]] = plot.ecosystems.points.presentations(data = data_for_plotting,
                                                      ecosystem_type_selected = ecosystem_type_all[1:i],
                                                      response_variable_selected) +
    theme(plot.margin = unit(c(ggarrange_margin_left,
                               ggarrange_margin_right,
                               ggarrange_margin_bottom,
                               ggarrange_margin_left),
                             "cm"),
          legend.position = "none") +
    scale_y_continuous(labels = scales::number_format(accuracy = 0.01)) + 
    xlim(x_min, x_max) +
    ylim(y_min, y_max)
  
  }
# --- COMBINE PLOTS --- #

# Define parameters

p_combined = NULL
p_combined[[1]] = plots[[1]]

# Combine plots

for(i in 1:length(ecosystem_type_all)+1){
  
  p_combined[[i]] = ggarrange(plots[[i]] +
                                theme(axis.text = element_text(size = presentation_axes_size)) + 
                                font("legend.text", size = size_legend) +
                                font("xlab", size = size_y_axis) +
                                font("ylab", size = size_y_axis),
                              nrow = 1,
                              align = "v",
                              label.x = 0.1,
                              label.y = 0.8)

  }
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## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).
# --- SAVE COMBINED PLOTS --- #

for(i in 1:length(ecosystem_type_all)+1){
  
  png(file = here("3_results", 
                  "figures", 
                  disturbance_selected, 
                  "presentations", 
                  paste0("ecosystems_connected_diversity_", i, ".png")),
      width = presentation_figure_width,
      height = presentation_figure_height,
      units = presentation_figure_units,
      res = presentation_figure_res)
  
  print(p_combined[[i]])
  
  dev.off()
  
  }

Analysis scripts

Video analysis

To analyse the videos I took of the ecosystems, I used the package BEMOVI. For this, I had to use the powerful computer. Below is the code utilised for video analysis on the powerful computer.

# Clear workspace
rm(list = ls())

# Set working directory
setwd("/media/mendel-himself/ID_061_Ema2/PatchSizePilot/training")

# Load required libraries
# library(devtools)
# install_github("femoerman/bemovi", ref="master")
library(bemovi)
library(parallel)
library(doParallel)
library(foreach)

# Define memory allocation parameters (in MB)
memory.alloc <- 240000           # Total memory allocated
memory.per.identifier <- 40000   # Memory per identifier
memory.per.linker <- 5000        # Memory per linker
memory.per.overlay <- 60000      # Memory per overlay

# Set paths for tools and particle linker
tools.path <- "/home/mendel-himself/bemovi_tools/" # Path to tools folder
to.particlelinker <- tools.path

# Set directories and file names
to.data <- paste(getwd(), "/", sep = "")
video.description.folder <- "0_video_description/"
video.description.file <- "video_description.txt"
raw.video.folder <- "1_raw/"
raw.avi.folder <- "1a_raw_avi/"
metadata.folder <- "1b_raw_meta/"
particle.data.folder <- "2_particle_data/"
trajectory.data.folder <- "3_trajectory_data/"
temp.overlay.folder <- "4a_temp_overlays/"
overlay.folder <- "4_overlays/"
merged.data.folder <- "5_merged_data/"
ijmacs.folder <- "ijmacs/"

######################################################################
# VIDEO PARAMETERS

# Define video parameters
fps <- 25                  # Video frame rate (frames per second)
total_frames <- 125        # Total length of video (frames)
width <- 2048              # Video width (pixels)
height <- 2048             # Video height (pixels)
measured_volume <- 34.4    # Measured volume (microliters) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
pixel_to_scale <- 4.05     # Size of a pixel (micrometers) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
video.format <- "cxd"      # Video file format (avi, cxd, mov, tiff)
difference.lag <- 10       # Difference lag
thresholds <- c(13, 255)   # Threshold values of pixel intensity (considered a measure of pixel "whiteness") for determining if a pixel belongs to an individual rather than the background

######################################################################
# FILTERING PARAMETERS
# optimized for Perfex Pro 10 stereomicrocope with Perfex SC38800 (IDS UI-3880LE-M-GL) camera
# tested stereomicroscopes: Perfex Pro 10, Nikon SMZ1500, Leica M205 C
# tested cameras: Perfex SC38800, Canon 5D Mark III, Hamamatsu Orca Flash 4
# tested species: Tet, Col, Pau, Pca, Eug, Chi, Ble, Ceph, Lox, Spi

particle_min_size <- 10           # Minimum particle size (pixels)
particle_max_size <- 1000         # Maximum particle size (pixels)
trajectory_link_range <- 3        # Number of adjacent frames for linking particles
trajectory_displacement <- 16     # Maximum displacement of a particle between frames

# Filtering criteria
filter_min_net_disp <- 25         # Minimum net displacement (µm)
filter_min_duration <- 1          # Minimum duration (s)
filter_detection_freq <- 0.1      # Minimum detection frequency (1/s)
filter_median_step_length <- 3    # Minimum median step length (µm)

######################################################################
# VIDEO ANALYSIS

# Check if all tools are installed and set permissions
check_tools_folder(tools.path)
system(paste0("chmod a+x ", tools.path, "bftools/bf.sh"))
system(paste0("chmod a+x ", tools.path, "bftools/bfconvert"))
system(paste0("chmod a+x ", tools.path, "bftools/showinf"))

# Convert video files to compressed avi format
convert_to_avi(to.data,
               raw.video.folder,
               raw.avi.folder,
               metadata.folder,
               tools.path,
               fps,
               video.format)


# Uncomment the following lines for testing
# check_video_file_names(to.data, raw.avi.folder, video.description.folder, video.description.file)
# check_threshold_values(to.data, raw.avi.folder, ijmacs.folder, 2, difference.lag, thresholds, tools.path, memory.alloc)

# Identify particles in the video
locate_and_measure_particles(to.data,
                             raw.avi.folder,
                             particle.data.folder,
                             difference.lag,
                             min_size = particle_min_size,
                             max_size = particle_max_size,
                             thresholds = thresholds,
                             tools.path,
                             memory = memory.alloc,
                             memory.per.identifier = memory.per.identifier,
                             max.cores = detectCores() - 1)

# Link particles across frames to form trajectories
link_particles(to.data,
               particle.data.folder,
               trajectory.data.folder,
               linkrange = trajectory_link_range,
               disp = trajectory_displacement,
               start_vid = 1,
               memory = memory.alloc,
               memory_per_linkerProcess = memory.per.linker,
               raw.avi.folder,
               max.cores = detectCores() - 1,
               max_time = 1)

# Merge video description file with particle data
merge_data(to.data,
           particle.data.folder,
           trajectory.data.folder,
           video.description.folder,
           video.description.file,
           merged.data.folder)

# Load the merged data
load(paste0(to.data, merged.data.folder, "Master.RData"))

# Filter trajectory data based on defined criteria
trajectory.data.filtered <- filter_data(trajectory.data,
                                        filter_min_net_disp,
                                        filter_min_duration,
                                        filter_detection_freq,
                                        filter_median_step_length)

# Summarize trajectory data to individual-based data
morph_mvt <- summarize_trajectories(trajectory.data.filtered,
                                    calculate.median = F,
                                    write = T,
                                    to.data,
                                    merged.data.folder)

# Summarize sample level data
summarize_populations(trajectory.data.filtered,
                      morph_mvt,
                      write = T,
                      to.data,
                      merged.data.folder,
                      video.description.folder,
                      video.description.file,
                      total_frames)

# Create overlays for validation
create.subtitle.overlays(to.data,
                         traj.data = trajectory.data.filtered,
                         raw.video.folder,
                         raw.avi.folder,
                         temp.overlay.folder,
                         overlay.folder,
                         fps,
                         vid.length = total_frames / fps,
                         width,
                         height,
                         tools.path = tools.path,
                         overlay.type = "number",
                         video.format)

# Create overlays (old method)
create_overlays(traj.data = trajectory.data.filtered,
                to.data = to.data,
                merged.data.folder = merged.data.folder,
                raw.video.folder = raw.avi.folder,
                temp.overlay.folder = "4a_temp_overlays_old/",
                overlay.folder = "4_overlays_old/",
                width = width,
                height = height,
                difference.lag = difference.lag,
                type = "traj",
                predict_spec = F,
                contrast.enhancement = 1,
                IJ.path = "/home/mendel-himself/bemovi_tools",
                memory = memory.alloc,
                max.cores = detectCores() - 1,
                memory.per.overlay = memory.per.overlay)

Species identification

To avoid transferring all the data from the powerful computer, I performed species identification on that system and subsequently imported the results into the Rstudio folder on my personal computer. Below is the code utilised for species identification on the powerful computer.

# Clear the workspace
rm(list = ls())

# Uncomment and install required packages if not already installed
#install.packages("e1071",dependencies = T)
#install.packages("devtools",dependencies = T)
#install_github("pennekampster/bemovi", ref="master")
#library(devtools)

# Load required libraries
library(bemovi)
library(e1071)
library("here")
library("tidyverse")

# Define time points in the experiment
time_points_in_experiment = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")

# Loop through each time point in the experiment
for (time_point in time_points_in_experiment) {
  
  # Define folder names and paths
  video.description.folder = "0_video_description/"
  video.description.file = "video_description.txt"
  merged.data.folder = "5_merged_data/"
  monocultures_folder_path = here("biomass_analysis", "training", "")
  mixed_cultures_folder_path = here("biomass_analysis", time_point, "")
  
  #Parameters used in the video analysis script
  fps = 25
  nsv = 5
  measured_volume = 34.4
  pixel_to_scale = 4.05
  filter_min_net_disp = 25
  filter_min_duration = 1
  filter_detection_freq = 0.1
  filter_median_step_length = 3
  
  # Load master dataset of mono-cultures
  load(paste0(monocultures_folder_path, merged.data.folder, "Master.RData"))
  trajectory.data_monocultures = trajectory.data
  rm(trajectory.data)
  
  # Filter the master data of mono-cultures using the same parameters as in the video analysis script
  trajectory.data_monocultures.filtered = filter_data(trajectory.data_monocultures,
                                                      filter_min_net_disp,
                                                      filter_min_duration,
                                                      filter_detection_freq,
                                                      filter_median_step_length)
  
  # Summarize trajectory data to individual-based data
  morph_mvt = summarize_trajectories(data = trajectory.data_monocultures.filtered,
                                     calculate.median = FALSE,
                                     write = TRUE,
                                     to.data = monocultures_folder_path,
                                     merged.data.folder = merged.data.folder) %>%
    mutate(comment = NULL)
  
  # Prepare training data by removing incomplete cases
  training_data = morph_mvt[complete.cases(morph_mvt), ]
  
  # Train SVM model on the training data
  svm1 = svm(
    factor(species) ~
      mean_grey +
      sd_grey +
      mean_area +
      sd_area +
      mean_perimeter +
      mean_turning +
      sd_turning +
      sd_perimeter +
      mean_major +
      sd_major +
      mean_minor +
      sd_minor +
      mean_ar +
      sd_ar +
      duration +
      max_net  +
      net_disp +
      net_speed +
      gross_disp +
      max_step +
      min_step +
      sd_step +
      sd_gross_speed +
      max_gross_speed +
      min_gross_speed ,
    data = training_data,
    probability = T,
    na.action = na.pass)
  
  # Generate and print confusion matrix
  confusion.matrix = table(svm1$fitted, training_data$species)
  confusion.matrix.nd = confusion.matrix
  diag(confusion.matrix.nd) = 0
  svm1$confusion = cbind(confusion.matrix,
                         class.error = rowSums(confusion.matrix.nd) / rowSums(confusion.matrix))
  
  print(paste("Confusion matrix of time point", time_point))
  print(svm1$confusion)
  
  # Extract unique species names
  species.names = unique(trajectory.data_monocultures$species)
  
  # Load mixed cultures dataset
  load(paste0(mixed_cultures_folder_path, merged.data.folder, "Master.RData"))
  trajectory.data_mixed = trajectory.data
  rm(trajectory.data)
  
  # Filter mixed cultures data using the same parameters
  trajectory.data_mixed.filtered = filter_data(trajectory.data_mixed,
                                               filter_min_net_disp,
                                               filter_min_duration,
                                               filter_detection_freq,
                                               filter_median_step_length)
  
  # Summarize trajectory data to individual-based data
  morph_mvt = summarize_trajectories(data = trajectory.data_mixed.filtered,
                                     calculate.median = FALSE,
                                     write = TRUE,
                                     to.data = mixed_cultures_folder_path,
                                     merged.data.folder = merged.data.folder)[, which(colnames(morph_mvt) != "Col_manual")] %>%
    mutate(comment = NULL)
  
  # Prepare data for prediction by removing incomplete cases
  data.to.predict = morph_mvt[complete.cases(morph_mvt),]
  
  # Predict species using the trained SVM model
  p.id = predict(object = svm1, data.to.predict, type = "response")
  data.to.predict$predicted_species = as.character(p.id)
  
  # Summarize population data
  pop.data = summarize_populations(traj.data = trajectory.data_monocultures.filtered,
                                   sum.data = morph_mvt,
                                   write = TRUE,
                                   to.data = mixed_cultures_folder_path,
                                   merged.data.folder = merged.data.folder,
                                   video.description.folder = video.description.folder,
                                   video.description.file = video.description.file,
                                   total_frame = fps * nsv)
  
  # Function to calculate species density
  species.density = function(sample_output,
                             indiv_predicted,
                             species_names,
                             total_frames,
                             mv = measured_volume) {
    samples = unique(indiv_predicted$file)
    
    sp.dens = matrix(0,
                     nrow(sample_output),
                     length(species_names))
    
    colnames(sp.dens) = species_names
    
    for (i in 1:length(samples)) {
      indiv = subset(indiv_predicted, file == samples[i])
      
      spec = unique(indiv$predicted_species)
      
      for (j in 1:length(spec)) {
        all.indiv.sp = subset(indiv,
                              predicted_species == spec[j])
        
        dens = sum(all.indiv.sp$N_frames) / total_frames / mv
        sp.dens[which(sample_output$file == as.character(samples[i])), which(species_names == spec[j])] = dens
      }
    }
    
    return(cbind(sample_output, sp.dens))
    
  }
  
  # Calculate species density for the current time point
  output = species.density(pop.data,
                           data.to.predict,
                           species.names,
                           total_frames = fps * nsv,
                           mv = measured_volume)
  
  # Save the species density results to a CSV file
  file_name = paste0("species_ID_", time_point, ".csv")
  write.csv(output, here("biomass_analysis", "species_ID_results", file_name))
  rm(output)
  
}

Other

Running time

## Time difference of 1.9 mins

Useful code

If you want to change a certain part of the code using the following code in Unix:

#Rmd script
cd /Users/Ema/Documents/Github/PatchSize/3_r_files
sed -i '' 's/old_string/new_string/g' *.Rmd

#R script
cd /Users/ema/Documents/GitHub/PatchSize/3_r_files/functions
sed -i '' 's/old_string/new_string/g' *.R

you want to share a dataset and get a reproducible object, use the following R code:

dput()

Crashed cultures

The only type of ecosystem where all cultures crashed was small connected to small at high disturbance.

R version

R.version.string
## [1] "R version 4.3.2 (2023-10-31)"

R package versions

The R packages we used with their version are as follows:

sessionInfo()
## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.2.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: Europe/Zurich
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] conflicted_1.2.0    broom.mixed_0.2.9.5 emmeans_1.10.4     
##  [4] combinat_0.0-8      Rmisc_1.5.1         betapart_1.6       
##  [7] vegan_2.6-6.1       lattice_0.22-6      permute_0.9-7      
## [10] glmmTMB_1.1.10      lmerTest_3.1-3      lme4_1.1-35.4      
## [13] Matrix_1.6-5        DHARMa_0.4.7        GGally_2.2.1       
## [16] gridExtra_2.3       plotly_4.10.4       ggpubr_0.6.0       
## [19] lubridate_1.9.3     forcats_1.0.0       stringr_1.5.1      
## [22] dplyr_1.1.4         purrr_1.0.2         readr_2.1.5        
## [25] tidyr_1.3.1         tibble_3.2.1        ggplot2_3.5.1      
## [28] tidyverse_2.0.0     plyr_1.8.9          renv_1.0.7.9000    
## [31] testthat_3.2.1.1    here_1.0.1         
## 
## loaded via a namespace (and not attached):
##   [1] RColorBrewer_1.1-3  rstudioapi_0.16.0   jsonlite_1.8.8     
##   [4] magrittr_2.0.3      estimability_1.5.1  farver_2.1.2       
##   [7] nloptr_2.1.1        rmarkdown_2.27      vctrs_0.6.5        
##  [10] memoise_2.0.1       minqa_1.2.7         rstatix_0.7.2      
##  [13] htmltools_0.5.8.1   itertools_0.1-3     broom_1.0.6        
##  [16] sass_0.4.9          parallelly_1.38.0   bslib_0.7.0        
##  [19] desc_1.4.3          htmlwidgets_1.6.4   cachem_1.1.0       
##  [22] TMB_1.9.15          mime_0.12           lifecycle_1.0.4    
##  [25] minpack.lm_1.2-4    iterators_1.0.14    pkgconfig_2.0.3    
##  [28] gap_1.6             R6_2.5.1            fastmap_1.2.0      
##  [31] shiny_1.9.1         rbibutils_2.2.16    future_1.34.0      
##  [34] magic_1.6-1         digest_0.6.36       numDeriv_2016.8-1.1
##  [37] colorspace_2.1-0    furrr_0.3.1         rprojroot_2.0.4    
##  [40] pkgload_1.3.4       qgam_1.3.4          labeling_0.4.3     
##  [43] fansi_1.0.6         timechange_0.3.0    httr_1.4.7         
##  [46] abind_1.4-5         mgcv_1.9-0          compiler_4.3.2     
##  [49] doParallel_1.0.17   withr_3.0.0         backports_1.5.0    
##  [52] carData_3.0-5       ggstats_0.6.0       highr_0.11         
##  [55] ggsignif_0.6.4      MASS_7.3-60         tools_4.3.2        
##  [58] ape_5.8             httpuv_1.6.15       glue_1.7.0         
##  [61] rcdd_1.6            promises_1.3.0      nlme_3.1-163       
##  [64] grid_4.3.2          cluster_2.1.4       generics_0.1.3     
##  [67] snow_0.4-4          gtable_0.3.5        tzdb_0.4.0         
##  [70] data.table_1.15.4   hms_1.1.3           car_3.1-2          
##  [73] utf8_1.2.4          foreach_1.5.2       pillar_1.9.0       
##  [76] later_1.3.2         splines_4.3.2       tidyselect_1.2.1   
##  [79] knitr_1.47          reformulas_0.3.0    xfun_0.45          
##  [82] brio_1.1.5          stringi_1.8.4       lazyeval_0.2.2     
##  [85] yaml_2.3.8          boot_1.3-30         evaluate_0.24.0    
##  [88] codetools_0.2-20    cli_3.6.3           xtable_1.8-4       
##  [91] geometry_0.4.7      Rdpack_2.6.1        munsell_0.5.1      
##  [94] jquerylib_0.1.4     Rcpp_1.0.12         doSNOW_1.0.20      
##  [97] globals_0.16.3      coda_0.19-4.1       parallel_4.3.2     
## [100] picante_1.8.2       gap.datasets_0.0.6  listenv_0.9.1      
## [103] viridisLite_0.4.2   mvtnorm_1.3-1       scales_1.3.0       
## [106] rlang_1.1.4         cowplot_1.1.3       fastmatch_1.1-4    
## [109] waldo_0.5.2

References